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Simplifying 4x2 + -7x + -87 = 0 Reorder the terms: -87 + -7x + 4x2 = 0 Solving -87 + -7x + 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'. -21.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '21.75' to each side of the equation. -21.75 + -1.75x + 21.75 + x2 = 0 + 21.75 Reorder the terms: -21.75 + 21.75 + -1.75x + x2 = 0 + 21.75 Combine like terms: -21.75 + 21.75 = 0.00 0.00 + -1.75x + x2 = 0 + 21.75 -1.75x + x2 = 0 + 21.75 Combine like terms: 0 + 21.75 = 21.75 -1.75x + x2 = 21.75 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 21.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 21.75 + 0.765625 Combine like terms: 21.75 + 0.765625 = 22.515625 0.765625 + -1.75x + x2 = 22.515625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 22.515625 Calculate the square root of the right side: 4.745063224 Break this problem into two subproblems by setting (x + -0.875) equal to 4.745063224 and -4.745063224.Subproblem 1
x + -0.875 = 4.745063224 Simplifying x + -0.875 = 4.745063224 Reorder the terms: -0.875 + x = 4.745063224 Solving -0.875 + x = 4.745063224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 4.745063224 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 4.745063224 + 0.875 x = 4.745063224 + 0.875 Combine like terms: 4.745063224 + 0.875 = 5.620063224 x = 5.620063224 Simplifying x = 5.620063224Subproblem 2
x + -0.875 = -4.745063224 Simplifying x + -0.875 = -4.745063224 Reorder the terms: -0.875 + x = -4.745063224 Solving -0.875 + x = -4.745063224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -4.745063224 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -4.745063224 + 0.875 x = -4.745063224 + 0.875 Combine like terms: -4.745063224 + 0.875 = -3.870063224 x = -3.870063224 Simplifying x = -3.870063224Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.620063224, -3.870063224}
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