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Simplifying 8x2 + 12x + -18 = 0 Reorder the terms: -18 + 12x + 8x2 = 0 Solving -18 + 12x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 6x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 6x + 4x2)' equal to zero and attempt to solve: Simplifying -9 + 6x + 4x2 = 0 Solving -9 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 1.5x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 1.5x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 1.5x + x2 = 0 + 2.25 1.5x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 1.5x + x2 = 2.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 2.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 2.25 + 0.5625 Combine like terms: 2.25 + 0.5625 = 2.8125 0.5625 + 1.5x + x2 = 2.8125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x + 0.75) equal to 1.677050983 and -1.677050983.Subproblem 1
x + 0.75 = 1.677050983 Simplifying x + 0.75 = 1.677050983 Reorder the terms: 0.75 + x = 1.677050983 Solving 0.75 + x = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.677050983 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.677050983 + -0.75 x = 1.677050983 + -0.75 Combine like terms: 1.677050983 + -0.75 = 0.927050983 x = 0.927050983 Simplifying x = 0.927050983Subproblem 2
x + 0.75 = -1.677050983 Simplifying x + 0.75 = -1.677050983 Reorder the terms: 0.75 + x = -1.677050983 Solving 0.75 + x = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.677050983 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.677050983 + -0.75 x = -1.677050983 + -0.75 Combine like terms: -1.677050983 + -0.75 = -2.427050983 x = -2.427050983 Simplifying x = -2.427050983Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.927050983, -2.427050983}Solution
x = {0.927050983, -2.427050983}
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