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Simplifying 2x2 + 6x = 58 Reorder the terms: 6x + 2x2 = 58 Solving 6x + 2x2 = 58 Solving for variable 'x'. Reorder the terms: -58 + 6x + 2x2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + 3x + x2)' equal to zero and attempt to solve: Simplifying -29 + 3x + x2 = 0 Solving -29 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 3x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 3x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 3x + x2 = 0 + 29 3x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 3x + x2 = 29 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 29 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 29 + 2.25 Combine like terms: 29 + 2.25 = 31.25 2.25 + 3x + x2 = 31.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + 1.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + 1.5 = 5.590169944 Simplifying x + 1.5 = 5.590169944 Reorder the terms: 1.5 + x = 5.590169944 Solving 1.5 + x = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5.590169944 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.590169944 + -1.5 x = 5.590169944 + -1.5 Combine like terms: 5.590169944 + -1.5 = 4.090169944 x = 4.090169944 Simplifying x = 4.090169944Subproblem 2
x + 1.5 = -5.590169944 Simplifying x + 1.5 = -5.590169944 Reorder the terms: 1.5 + x = -5.590169944 Solving 1.5 + x = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5.590169944 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.590169944 + -1.5 x = -5.590169944 + -1.5 Combine like terms: -5.590169944 + -1.5 = -7.090169944 x = -7.090169944 Simplifying x = -7.090169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.090169944, -7.090169944}Solution
x = {4.090169944, -7.090169944}
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