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Simplifying 7x + -2x(x + -10) = 40 Reorder the terms: 7x + -2x(-10 + x) = 40 7x + (-10 * -2x + x * -2x) = 40 7x + (20x + -2x2) = 40 Combine like terms: 7x + 20x = 27x 27x + -2x2 = 40 Solving 27x + -2x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + 27x + -2x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 27x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 20 + -13.5x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -13.5x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -13.5x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -13.5x + x2 = 0 + -20 -13.5x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -13.5x + x2 = -20 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -20 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -20 + 45.5625 Combine like terms: -20 + 45.5625 = 25.5625 45.5625 + -13.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -6.75) equal to 5.055937104 and -5.055937104.Subproblem 1
x + -6.75 = 5.055937104 Simplifying x + -6.75 = 5.055937104 Reorder the terms: -6.75 + x = 5.055937104 Solving -6.75 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 5.055937104 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 5.055937104 + 6.75 x = 5.055937104 + 6.75 Combine like terms: 5.055937104 + 6.75 = 11.805937104 x = 11.805937104 Simplifying x = 11.805937104Subproblem 2
x + -6.75 = -5.055937104 Simplifying x + -6.75 = -5.055937104 Reorder the terms: -6.75 + x = -5.055937104 Solving -6.75 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -5.055937104 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -5.055937104 + 6.75 x = -5.055937104 + 6.75 Combine like terms: -5.055937104 + 6.75 = 1.694062896 x = 1.694062896 Simplifying x = 1.694062896Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.805937104, 1.694062896}
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