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Simplifying 2x2 + 3x + -63 = 0 Reorder the terms: -63 + 3x + 2x2 = 0 Solving -63 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + 1.5x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + 1.5x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + 1.5x + x2 = 0 + 31.5 1.5x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 1.5x + x2 = 31.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 31.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 31.5 + 0.5625 Combine like terms: 31.5 + 0.5625 = 32.0625 0.5625 + 1.5x + x2 = 32.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 32.0625 Calculate the square root of the right side: 5.662375826 Break this problem into two subproblems by setting (x + 0.75) equal to 5.662375826 and -5.662375826.Subproblem 1
x + 0.75 = 5.662375826 Simplifying x + 0.75 = 5.662375826 Reorder the terms: 0.75 + x = 5.662375826 Solving 0.75 + x = 5.662375826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 5.662375826 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 5.662375826 + -0.75 x = 5.662375826 + -0.75 Combine like terms: 5.662375826 + -0.75 = 4.912375826 x = 4.912375826 Simplifying x = 4.912375826Subproblem 2
x + 0.75 = -5.662375826 Simplifying x + 0.75 = -5.662375826 Reorder the terms: 0.75 + x = -5.662375826 Solving 0.75 + x = -5.662375826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -5.662375826 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -5.662375826 + -0.75 x = -5.662375826 + -0.75 Combine like terms: -5.662375826 + -0.75 = -6.412375826 x = -6.412375826 Simplifying x = -6.412375826Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.912375826, -6.412375826}
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