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Simplifying 4x2 + -3x + -189 = 0 Reorder the terms: -189 + -3x + 4x2 = 0 Solving -189 + -3x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -47.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '47.25' to each side of the equation. -47.25 + -0.75x + 47.25 + x2 = 0 + 47.25 Reorder the terms: -47.25 + 47.25 + -0.75x + x2 = 0 + 47.25 Combine like terms: -47.25 + 47.25 = 0.00 0.00 + -0.75x + x2 = 0 + 47.25 -0.75x + x2 = 0 + 47.25 Combine like terms: 0 + 47.25 = 47.25 -0.75x + x2 = 47.25 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 = 47.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 47.25 + 0.140625 Combine like terms: 47.25 + 0.140625 = 47.390625 0.140625 + -0.75x + x2 = 47.390625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 47.390625 Calculate the square root of the right side: 6.884084907 Break this problem into two subproblems by setting (x + -0.375) equal to 6.884084907 and -6.884084907.Subproblem 1
x + -0.375 = 6.884084907 Simplifying x + -0.375 = 6.884084907 Reorder the terms: -0.375 + x = 6.884084907 Solving -0.375 + x = 6.884084907 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 = 6.884084907 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 6.884084907 + 0.375 x = 6.884084907 + 0.375 Combine like terms: 6.884084907 + 0.375 = 7.259084907 x = 7.259084907 Simplifying x = 7.259084907Subproblem 2
x + -0.375 = -6.884084907 Simplifying x + -0.375 = -6.884084907 Reorder the terms: -0.375 + x = -6.884084907 Solving -0.375 + x = -6.884084907 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 = -6.884084907 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -6.884084907 + 0.375 x = -6.884084907 + 0.375 Combine like terms: -6.884084907 + 0.375 = -6.509084907 x = -6.509084907 Simplifying x = -6.509084907Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.259084907, -6.509084907}
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