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Simplifying 12x2 + 24x + -9 = 0 Reorder the terms: -9 + 24x + 12x2 = 0 Solving -9 + 24x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 8x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying -3 + 8x + 4x2 = 0 Solving -3 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 2x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 2x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 2x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 2x + x2 = 0 + 0.75 2x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 2x + x2 = 0.75 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 = 0.75 + 1 Reorder the terms: 1 + 2x + x2 = 0.75 + 1 Combine like terms: 0.75 + 1 = 1.75 1 + 2x + x2 = 1.75 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + 1) equal to 1.322875656 and -1.322875656.Subproblem 1
x + 1 = 1.322875656 Simplifying x + 1 = 1.322875656 Reorder the terms: 1 + x = 1.322875656 Solving 1 + x = 1.322875656 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 = 1.322875656 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.322875656 + -1 x = 1.322875656 + -1 Combine like terms: 1.322875656 + -1 = 0.322875656 x = 0.322875656 Simplifying x = 0.322875656Subproblem 2
x + 1 = -1.322875656 Simplifying x + 1 = -1.322875656 Reorder the terms: 1 + x = -1.322875656 Solving 1 + x = -1.322875656 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 = -1.322875656 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.322875656 + -1 x = -1.322875656 + -1 Combine like terms: -1.322875656 + -1 = -2.322875656 x = -2.322875656 Simplifying x = -2.322875656Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.322875656, -2.322875656}Solution
x = {0.322875656, -2.322875656}
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