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Simplifying 2x2 + 4x + -340 = 0 Reorder the terms: -340 + 4x + 2x2 = 0 Solving -340 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-170 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-170 + 2x + x2)' equal to zero and attempt to solve: Simplifying -170 + 2x + x2 = 0 Solving -170 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 2x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 2x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 2x + x2 = 0 + 170 2x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 2x + x2 = 170 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 170 + 1 Reorder the terms: 1 + 2x + x2 = 170 + 1 Combine like terms: 170 + 1 = 171 1 + 2x + x2 = 171 Factor a perfect square on the left side: (x + 1)(x + 1) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + 1) equal to 13.076696831 and -13.076696831.Subproblem 1
x + 1 = 13.076696831 Simplifying x + 1 = 13.076696831 Reorder the terms: 1 + x = 13.076696831 Solving 1 + x = 13.076696831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 13.076696831 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.076696831 + -1 x = 13.076696831 + -1 Combine like terms: 13.076696831 + -1 = 12.076696831 x = 12.076696831 Simplifying x = 12.076696831Subproblem 2
x + 1 = -13.076696831 Simplifying x + 1 = -13.076696831 Reorder the terms: 1 + x = -13.076696831 Solving 1 + x = -13.076696831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -13.076696831 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.076696831 + -1 x = -13.076696831 + -1 Combine like terms: -13.076696831 + -1 = -14.076696831 x = -14.076696831 Simplifying x = -14.076696831Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.076696831, -14.076696831}Solution
x = {12.076696831, -14.076696831}
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