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Simplifying (2x * 2x) + 5x + -12 = 0 Reorder the terms for easier multiplication: (2 * 2x * x) + 5x + -12 = 0 Multiply 2 * 2 (4x * x) + 5x + -12 = 0 Multiply x * x (4x2) + 5x + -12 = 0 Reorder the terms: -12 + 5x + (4x2) = 0 Solving -12 + 5x + (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'. -3 + 1.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.25x + x2 = 0 + 3 1.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.25x + x2 = 3 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 3 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 3 + 0.390625 Combine like terms: 3 + 0.390625 = 3.390625 0.390625 + 1.25x + x2 = 3.390625 Factor a perfect square on the left side: ((x) + 0.625)((x) + 0.625) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting ((x) + 0.625) equal to 1.841364983 and -1.841364983.Subproblem 1
(x) + 0.625 = 1.841364983 Simplifying (x) + 0.625 = 1.841364983 x + 0.625 = 1.841364983 Reorder the terms: 0.625 + x = 1.841364983 Solving 0.625 + x = 1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.841364983 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.841364983 + -0.625 x = 1.841364983 + -0.625 Combine like terms: 1.841364983 + -0.625 = 1.216364983 x = 1.216364983 Simplifying x = 1.216364983Subproblem 2
(x) + 0.625 = -1.841364983 Simplifying (x) + 0.625 = -1.841364983 x + 0.625 = -1.841364983 Reorder the terms: 0.625 + x = -1.841364983 Solving 0.625 + x = -1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.841364983 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.841364983 + -0.625 x = -1.841364983 + -0.625 Combine like terms: -1.841364983 + -0.625 = -2.466364983 x = -2.466364983 Simplifying x = -2.466364983Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.216364983, -2.466364983}
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