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Simplifying 10x2 + 40x + 15 = 0 Reorder the terms: 15 + 40x + 10x2 = 0 Solving 15 + 40x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + 8x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 8x + 2x2 = 0 Solving 3 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 4x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 4x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 4x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 4x + x2 = 0 + -1.5 4x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 4x + x2 = -1.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.5 + 4 Reorder the terms: 4 + 4x + x2 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + 4x + x2 = 2.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x + 2) equal to 1.58113883 and -1.58113883.Subproblem 1
x + 2 = 1.58113883 Simplifying x + 2 = 1.58113883 Reorder the terms: 2 + x = 1.58113883 Solving 2 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.58113883 + -2 x = 1.58113883 + -2 Combine like terms: 1.58113883 + -2 = -0.41886117 x = -0.41886117 Simplifying x = -0.41886117Subproblem 2
x + 2 = -1.58113883 Simplifying x + 2 = -1.58113883 Reorder the terms: 2 + x = -1.58113883 Solving 2 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.58113883 + -2 x = -1.58113883 + -2 Combine like terms: -1.58113883 + -2 = -3.58113883 x = -3.58113883 Simplifying x = -3.58113883Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.41886117, -3.58113883}Solution
x = {-0.41886117, -3.58113883}
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