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Simplifying -2x(x + -7) + 10x = 34 Reorder the terms: -2x(-7 + x) + 10x = 34 (-7 * -2x + x * -2x) + 10x = 34 (14x + -2x2) + 10x = 34 Reorder the terms: 14x + 10x + -2x2 = 34 Combine like terms: 14x + 10x = 24x 24x + -2x2 = 34 Solving 24x + -2x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + 24x + -2x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 24x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 12x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying -17 + 12x + -1x2 = 0 Solving -17 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 17 + -12x + x2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -12x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -12x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -12x + x2 = 0 + -17 -12x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -12x + x2 = -17 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -17 + 36 Reorder the terms: 36 + -12x + x2 = -17 + 36 Combine like terms: -17 + 36 = 19 36 + -12x + x2 = 19 Factor a perfect square on the left side: (x + -6)(x + -6) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -6) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -6 = 4.358898944 Simplifying x + -6 = 4.358898944 Reorder the terms: -6 + x = 4.358898944 Solving -6 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.358898944 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.358898944 + 6 x = 4.358898944 + 6 Combine like terms: 4.358898944 + 6 = 10.358898944 x = 10.358898944 Simplifying x = 10.358898944Subproblem 2
x + -6 = -4.358898944 Simplifying x + -6 = -4.358898944 Reorder the terms: -6 + x = -4.358898944 Solving -6 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.358898944 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.358898944 + 6 x = -4.358898944 + 6 Combine like terms: -4.358898944 + 6 = 1.641101056 x = 1.641101056 Simplifying x = 1.641101056Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.358898944, 1.641101056}Solution
x = {10.358898944, 1.641101056}
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