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By completing the square, find the solutions of x which satisfy the equation x^2+14x-1=0

Using the general complete the square formula, where x 2 +bx+c=0 becomes (a+b/2) 2 +b 2 +c=0, we get (x+7) 2 -7 2 -1=0 This can be rearranged to show that (x+7) 2 =50 by taking the square root of both sides ...
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Answered by Immie F. • Maths tutor
3421 Views

For the equation, 5(7x + 8) + 3(2x + b) ≡ ax + 13. Find the values of a and b. You may use a calculator.

By expanding the brackets on the left hand side of the equation you get,35x + 40 + 6x + 3b and by simplifying you get 41x + 40 + 3b.by comparing the x and constant terms on either side you find that a = 41, ...
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Answered by David B. • Maths tutor
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Solve the simultaneous equations algebraically: y = x+19 AND y = x^2 + 4x +1.

We have one linear and one quadratic equation here. Since we have a quadratic, we will have two sets of solutions. Let's solve by substitution. Substitute equation (1) into equation (2), which yields:x + 19 ...
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Answered by Liam D. • Maths tutor
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Three different brands of rice are on sale, which brand provides the best value for money? Their prices are: Brand A) 250g for £3.21, Brand B) 400g for £5.30, Brand C) 750g for £8.80

In order to compare the prices of each of these brands of rice, we will work out how much it costs to buy 100g of each brand - by using a consistent weight we can measure the prices against each other. The s...
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Answered by Gregory C. • Maths tutor
4130 Views

solve (y+1)^2 = 4

(y+1) 2 = 4. The power of two becomes a square root on the other side. Don't forget that this is plus or minus the square root of 4. Now we have y+1 = +- sqrt(4). We now have two equations to solve for y. y+...
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Answered by Jasper K. • Maths tutor
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