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Simplifying 2x2 + -5x + 9x = 12 Reorder the terms: -5x + 9x + 2x2 = 12 Combine like terms: -5x + 9x = 4x 4x + 2x2 = 12 Solving 4x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 4x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 2x + x2)' equal to zero and attempt to solve: Simplifying -6 + 2x + x2 = 0 Solving -6 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 2x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 2x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2x + x2 = 0 + 6 2x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 2x + x2 = 6 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 = 6 + 1 Reorder the terms: 1 + 2x + x2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + 2x + x2 = 7 Factor a perfect square on the left side: (x + 1)(x + 1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 1) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 1 = 2.645751311 Simplifying x + 1 = 2.645751311 Reorder the terms: 1 + x = 2.645751311 Solving 1 + x = 2.645751311 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 = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.645751311 + -1 x = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 x = 1.645751311 Simplifying x = 1.645751311Subproblem 2
x + 1 = -2.645751311 Simplifying x + 1 = -2.645751311 Reorder the terms: 1 + x = -2.645751311 Solving 1 + x = -2.645751311 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 = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.645751311 + -1 x = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 x = -3.645751311 Simplifying x = -3.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.645751311, -3.645751311}Solution
x = {1.645751311, -3.645751311}
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