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Simplifying 0 = 4x2 + 3x + -36 Reorder the terms: 0 = -36 + 3x + 4x2 Solving 0 = -36 + 3x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 36 = 36 36 + -3x + -4x2 = -36 + 3x + 4x2 + 36 + -3x + -4x2 Reorder the terms: 36 + -3x + -4x2 = -36 + 36 + 3x + -3x + 4x2 + -4x2 Combine like terms: -36 + 36 = 0 36 + -3x + -4x2 = 0 + 3x + -3x + 4x2 + -4x2 36 + -3x + -4x2 = 3x + -3x + 4x2 + -4x2 Combine like terms: 3x + -3x = 0 36 + -3x + -4x2 = 0 + 4x2 + -4x2 36 + -3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 36 + -3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -9 + 0.75x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 0.75x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 0.75x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 0.75x + x2 = 0 + 9 0.75x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 0.75x + x2 = 9 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 9 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 9 + 0.140625 Combine like terms: 9 + 0.140625 = 9.140625 0.140625 + 0.75x + x2 = 9.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 9.140625 Calculate the square root of the right side: 3.023346656 Break this problem into two subproblems by setting (x + 0.375) equal to 3.023346656 and -3.023346656.Subproblem 1
x + 0.375 = 3.023346656 Simplifying x + 0.375 = 3.023346656 Reorder the terms: 0.375 + x = 3.023346656 Solving 0.375 + x = 3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 3.023346656 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 3.023346656 + -0.375 x = 3.023346656 + -0.375 Combine like terms: 3.023346656 + -0.375 = 2.648346656 x = 2.648346656 Simplifying x = 2.648346656Subproblem 2
x + 0.375 = -3.023346656 Simplifying x + 0.375 = -3.023346656 Reorder the terms: 0.375 + x = -3.023346656 Solving 0.375 + x = -3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -3.023346656 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -3.023346656 + -0.375 x = -3.023346656 + -0.375 Combine like terms: -3.023346656 + -0.375 = -3.398346656 x = -3.398346656 Simplifying x = -3.398346656Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.648346656, -3.398346656}
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