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Simplifying 9x2 + 2 + -13x + -3x2 + -14x = 0 Reorder the terms: 2 + -13x + -14x + 9x2 + -3x2 = 0 Combine like terms: -13x + -14x = -27x 2 + -27x + 9x2 + -3x2 = 0 Combine like terms: 9x2 + -3x2 = 6x2 2 + -27x + 6x2 = 0 Solving 2 + -27x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.3333333333 + -4.5x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -4.5x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -4.5x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -4.5x + x2 = 0 + -0.3333333333 -4.5x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -4.5x + x2 = -0.3333333333 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -0.3333333333 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -0.3333333333 + 5.0625 Combine like terms: -0.3333333333 + 5.0625 = 4.7291666667 5.0625 + -4.5x + x2 = 4.7291666667 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 4.7291666667 Calculate the square root of the right side: 2.174664725 Break this problem into two subproblems by setting (x + -2.25) equal to 2.174664725 and -2.174664725.Subproblem 1
x + -2.25 = 2.174664725 Simplifying x + -2.25 = 2.174664725 Reorder the terms: -2.25 + x = 2.174664725 Solving -2.25 + x = 2.174664725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.174664725 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.174664725 + 2.25 x = 2.174664725 + 2.25 Combine like terms: 2.174664725 + 2.25 = 4.424664725 x = 4.424664725 Simplifying x = 4.424664725Subproblem 2
x + -2.25 = -2.174664725 Simplifying x + -2.25 = -2.174664725 Reorder the terms: -2.25 + x = -2.174664725 Solving -2.25 + x = -2.174664725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.174664725 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.174664725 + 2.25 x = -2.174664725 + 2.25 Combine like terms: -2.174664725 + 2.25 = 0.075335275 x = 0.075335275 Simplifying x = 0.075335275Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.424664725, 0.075335275}
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