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Simplifying 10x2 + 10x + -430 = 0 Reorder the terms: -430 + 10x + 10x2 = 0 Solving -430 + 10x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-43 + x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-43 + x + x2)' equal to zero and attempt to solve: Simplifying -43 + x + x2 = 0 Solving -43 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + x + x2 = 0 + 43 x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 x + x2 = 43 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. x + 0.25 + x2 = 43 + 0.25 Reorder the terms: 0.25 + x + x2 = 43 + 0.25 Combine like terms: 43 + 0.25 = 43.25 0.25 + x + x2 = 43.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + 0.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + 0.5 = 6.576473219 Simplifying x + 0.5 = 6.576473219 Reorder the terms: 0.5 + x = 6.576473219 Solving 0.5 + x = 6.576473219 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 = 6.576473219 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.576473219 + -0.5 x = 6.576473219 + -0.5 Combine like terms: 6.576473219 + -0.5 = 6.076473219 x = 6.076473219 Simplifying x = 6.076473219Subproblem 2
x + 0.5 = -6.576473219 Simplifying x + 0.5 = -6.576473219 Reorder the terms: 0.5 + x = -6.576473219 Solving 0.5 + x = -6.576473219 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 = -6.576473219 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.576473219 + -0.5 x = -6.576473219 + -0.5 Combine like terms: -6.576473219 + -0.5 = -7.076473219 x = -7.076473219 Simplifying x = -7.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.076473219, -7.076473219}Solution
x = {6.076473219, -7.076473219}
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