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Simplifying -5x2 + -37x + -10 = 0 Reorder the terms: -10 + -37x + -5x2 = 0 Solving -10 + -37x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 37x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 37x + 5x2)' equal to zero and attempt to solve: Simplifying 10 + 37x + 5x2 = 0 Solving 10 + 37x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 7.4x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 7.4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 7.4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7.4x + x2 = 0 + -2 7.4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 7.4x + x2 = -2 The x term is 7.4x. Take half its coefficient (3.7). Square it (13.69) and add it to both sides. Add '13.69' to each side of the equation. 7.4x + 13.69 + x2 = -2 + 13.69 Reorder the terms: 13.69 + 7.4x + x2 = -2 + 13.69 Combine like terms: -2 + 13.69 = 11.69 13.69 + 7.4x + x2 = 11.69 Factor a perfect square on the left side: (x + 3.7)(x + 3.7) = 11.69 Calculate the square root of the right side: 3.419064199 Break this problem into two subproblems by setting (x + 3.7) equal to 3.419064199 and -3.419064199.Subproblem 1
x + 3.7 = 3.419064199 Simplifying x + 3.7 = 3.419064199 Reorder the terms: 3.7 + x = 3.419064199 Solving 3.7 + x = 3.419064199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = 3.419064199 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = 3.419064199 + -3.7 x = 3.419064199 + -3.7 Combine like terms: 3.419064199 + -3.7 = -0.280935801 x = -0.280935801 Simplifying x = -0.280935801Subproblem 2
x + 3.7 = -3.419064199 Simplifying x + 3.7 = -3.419064199 Reorder the terms: 3.7 + x = -3.419064199 Solving 3.7 + x = -3.419064199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = -3.419064199 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = -3.419064199 + -3.7 x = -3.419064199 + -3.7 Combine like terms: -3.419064199 + -3.7 = -7.119064199 x = -7.119064199 Simplifying x = -7.119064199Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.280935801, -7.119064199}Solution
x = {-0.280935801, -7.119064199}
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