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Simplifying -5x2 + 100x + -15 = 0 Reorder the terms: -15 + 100x + -5x2 = 0 Solving -15 + 100x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 20x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying -3 + 20x + -1x2 = 0 Solving -3 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -20x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -20x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -20x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -20x + x2 = 0 + -3 -20x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -20x + x2 = -3 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -3 + 100 Reorder the terms: 100 + -20x + x2 = -3 + 100 Combine like terms: -3 + 100 = 97 100 + -20x + x2 = 97 Factor a perfect square on the left side: (x + -10)(x + -10) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + -10) equal to 9.848857802 and -9.848857802.Subproblem 1
x + -10 = 9.848857802 Simplifying x + -10 = 9.848857802 Reorder the terms: -10 + x = 9.848857802 Solving -10 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.848857802 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.848857802 + 10 x = 9.848857802 + 10 Combine like terms: 9.848857802 + 10 = 19.848857802 x = 19.848857802 Simplifying x = 19.848857802Subproblem 2
x + -10 = -9.848857802 Simplifying x + -10 = -9.848857802 Reorder the terms: -10 + x = -9.848857802 Solving -10 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.848857802 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.848857802 + 10 x = -9.848857802 + 10 Combine like terms: -9.848857802 + 10 = 0.151142198 x = 0.151142198 Simplifying x = 0.151142198Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.848857802, 0.151142198}Solution
x = {19.848857802, 0.151142198}
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