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Simplifying -10x2 + -26x + 24 = 0 Reorder the terms: 24 + -26x + -10x2 = 0 Solving 24 + -26x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -13x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -13x + -5x2)' equal to zero and attempt to solve: Simplifying 12 + -13x + -5x2 = 0 Solving 12 + -13x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + 2.6x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 2.6x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 2.6x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 2.6x + x2 = 0 + 2.4 2.6x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 2.6x + x2 = 2.4 The x term is 2.6x. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6x + 1.69 + x2 = 2.4 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 2.4 + 1.69 Combine like terms: 2.4 + 1.69 = 4.09 1.69 + 2.6x + x2 = 4.09 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + 1.3) equal to 2.022374842 and -2.022374842.Subproblem 1
x + 1.3 = 2.022374842 Simplifying x + 1.3 = 2.022374842 Reorder the terms: 1.3 + x = 2.022374842 Solving 1.3 + x = 2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 2.022374842 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 2.022374842 + -1.3 x = 2.022374842 + -1.3 Combine like terms: 2.022374842 + -1.3 = 0.722374842 x = 0.722374842 Simplifying x = 0.722374842Subproblem 2
x + 1.3 = -2.022374842 Simplifying x + 1.3 = -2.022374842 Reorder the terms: 1.3 + x = -2.022374842 Solving 1.3 + x = -2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -2.022374842 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -2.022374842 + -1.3 x = -2.022374842 + -1.3 Combine like terms: -2.022374842 + -1.3 = -3.322374842 x = -3.322374842 Simplifying x = -3.322374842Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.722374842, -3.322374842}Solution
x = {0.722374842, -3.322374842}
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