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Simplifying 3x + -4x2 = -25 Solving 3x + -4x2 = -25 Solving for variable 'x'. Reorder the terms: 25 + 3x + -4x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -0.75x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -0.75x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -0.75x + x2 = 0 + 6.25 -0.75x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -0.75x + x2 = 6.25 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 = 6.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 6.25 + 0.140625 Combine like terms: 6.25 + 0.140625 = 6.390625 0.140625 + -0.75x + x2 = 6.390625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (x + -0.375) equal to 2.527968552 and -2.527968552.Subproblem 1
x + -0.375 = 2.527968552 Simplifying x + -0.375 = 2.527968552 Reorder the terms: -0.375 + x = 2.527968552 Solving -0.375 + x = 2.527968552 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 = 2.527968552 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.527968552 + 0.375 x = 2.527968552 + 0.375 Combine like terms: 2.527968552 + 0.375 = 2.902968552 x = 2.902968552 Simplifying x = 2.902968552Subproblem 2
x + -0.375 = -2.527968552 Simplifying x + -0.375 = -2.527968552 Reorder the terms: -0.375 + x = -2.527968552 Solving -0.375 + x = -2.527968552 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 = -2.527968552 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.527968552 + 0.375 x = -2.527968552 + 0.375 Combine like terms: -2.527968552 + 0.375 = -2.152968552 x = -2.152968552 Simplifying x = -2.152968552Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.902968552, -2.152968552}
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