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Simplifying -10x2 + 50x + 12 = 0 Reorder the terms: 12 + 50x + -10x2 = 0 Solving 12 + 50x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 25x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 25x + -5x2)' equal to zero and attempt to solve: Simplifying 6 + 25x + -5x2 = 0 Solving 6 + 25x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + -5x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -5x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -5x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -5x + x2 = 0 + 1.2 -5x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -5x + x2 = 1.2 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1.2 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.2 + 6.25 Combine like terms: 1.2 + 6.25 = 7.45 6.25 + -5x + x2 = 7.45 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.45 Calculate the square root of the right side: 2.729468813 Break this problem into two subproblems by setting (x + -2.5) equal to 2.729468813 and -2.729468813.Subproblem 1
x + -2.5 = 2.729468813 Simplifying x + -2.5 = 2.729468813 Reorder the terms: -2.5 + x = 2.729468813 Solving -2.5 + x = 2.729468813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.729468813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.729468813 + 2.5 x = 2.729468813 + 2.5 Combine like terms: 2.729468813 + 2.5 = 5.229468813 x = 5.229468813 Simplifying x = 5.229468813Subproblem 2
x + -2.5 = -2.729468813 Simplifying x + -2.5 = -2.729468813 Reorder the terms: -2.5 + x = -2.729468813 Solving -2.5 + x = -2.729468813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.729468813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.729468813 + 2.5 x = -2.729468813 + 2.5 Combine like terms: -2.729468813 + 2.5 = -0.229468813 x = -0.229468813 Simplifying x = -0.229468813Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.229468813, -0.229468813}Solution
x = {5.229468813, -0.229468813}
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