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Simplifying 4x2 + -3x + -63 = 0 Reorder the terms: -63 + -3x + 4x2 = 0 Solving -63 + -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'. -15.75 + -0.75x + x2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + -0.75x + 15.75 + x2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + -0.75x + x2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + -0.75x + x2 = 0 + 15.75 -0.75x + x2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 -0.75x + x2 = 15.75 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 = 15.75 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 15.75 + 0.140625 Combine like terms: 15.75 + 0.140625 = 15.890625 0.140625 + -0.75x + x2 = 15.890625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 15.890625 Calculate the square root of the right side: 3.98630468 Break this problem into two subproblems by setting (x + -0.375) equal to 3.98630468 and -3.98630468.Subproblem 1
x + -0.375 = 3.98630468 Simplifying x + -0.375 = 3.98630468 Reorder the terms: -0.375 + x = 3.98630468 Solving -0.375 + x = 3.98630468 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 = 3.98630468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 3.98630468 + 0.375 x = 3.98630468 + 0.375 Combine like terms: 3.98630468 + 0.375 = 4.36130468 x = 4.36130468 Simplifying x = 4.36130468Subproblem 2
x + -0.375 = -3.98630468 Simplifying x + -0.375 = -3.98630468 Reorder the terms: -0.375 + x = -3.98630468 Solving -0.375 + x = -3.98630468 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 = -3.98630468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -3.98630468 + 0.375 x = -3.98630468 + 0.375 Combine like terms: -3.98630468 + 0.375 = -3.61130468 x = -3.61130468 Simplifying x = -3.61130468Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.36130468, -3.61130468}
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