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Simplifying -5x2 + 8 + 2x + -10 + -9x2 = 0 Reorder the terms: 8 + -10 + 2x + -5x2 + -9x2 = 0 Combine like terms: 8 + -10 = -2 -2 + 2x + -5x2 + -9x2 = 0 Combine like terms: -5x2 + -9x2 = -14x2 -2 + 2x + -14x2 = 0 Solving -2 + 2x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + x + -7x2)' equal to zero and attempt to solve: Simplifying -1 + x + -7x2 = 0 Solving -1 + x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.1428571429 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -0.1428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -0.1428571429x + x2 = 0 + -0.1428571429 -0.1428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -0.1428571429x + x2 = -0.1428571429 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1428571429x + 0.25 + x2 = -0.1428571429 + 0.25 Reorder the terms: 0.25 + -0.1428571429x + x2 = -0.1428571429 + 0.25 Combine like terms: -0.1428571429 + 0.25 = 0.1071428571 0.25 + -0.1428571429x + x2 = 0.1071428571 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.1071428571 Calculate the square root of the right side: 0.327326835 Break this problem into two subproblems by setting (x + 0.5) equal to 0.327326835 and -0.327326835.Subproblem 1
x + 0.5 = 0.327326835 Simplifying x + 0.5 = 0.327326835 Reorder the terms: 0.5 + x = 0.327326835 Solving 0.5 + x = 0.327326835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.327326835 + -0.5 x = 0.327326835 + -0.5 Combine like terms: 0.327326835 + -0.5 = -0.172673165 x = -0.172673165 Simplifying x = -0.172673165Subproblem 2
x + 0.5 = -0.327326835 Simplifying x + 0.5 = -0.327326835 Reorder the terms: 0.5 + x = -0.327326835 Solving 0.5 + x = -0.327326835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.327326835 + -0.5 x = -0.327326835 + -0.5 Combine like terms: -0.327326835 + -0.5 = -0.827326835 x = -0.827326835 Simplifying x = -0.827326835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.172673165, -0.827326835}Solution
x = {-0.172673165, -0.827326835}
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