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Simplifying 4x2 + -6x + 9 = 25 Reorder the terms: 9 + -6x + 4x2 = 25 Solving 9 + -6x + 4x2 = 25 Solving for variable 'x'. Reorder the terms: 9 + -25 + -6x + 4x2 = 25 + -25 Combine like terms: 9 + -25 = -16 -16 + -6x + 4x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -16 + -6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -8 + -3x + 2x2 = 0 Solving -8 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -1.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.5x + x2 = 0 + 4 -1.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.5x + x2 = 4 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 = 4 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 4 + 0.5625 Combine like terms: 4 + 0.5625 = 4.5625 0.5625 + -1.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -0.75) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -0.75 = 2.136000936 Simplifying x + -0.75 = 2.136000936 Reorder the terms: -0.75 + x = 2.136000936 Solving -0.75 + x = 2.136000936 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 = 2.136000936 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.136000936 + 0.75 x = 2.136000936 + 0.75 Combine like terms: 2.136000936 + 0.75 = 2.886000936 x = 2.886000936 Simplifying x = 2.886000936Subproblem 2
x + -0.75 = -2.136000936 Simplifying x + -0.75 = -2.136000936 Reorder the terms: -0.75 + x = -2.136000936 Solving -0.75 + x = -2.136000936 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 = -2.136000936 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.136000936 + 0.75 x = -2.136000936 + 0.75 Combine like terms: -2.136000936 + 0.75 = -1.386000936 x = -1.386000936 Simplifying x = -1.386000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.886000936, -1.386000936}Solution
x = {2.886000936, -1.386000936}
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