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Simplifying 8x2 + 12x + -15 = 0 Reorder the terms: -15 + 12x + 8x2 = 0 Solving -15 + 12x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + 1.5x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 1.5x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 1.5x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 1.5x + x2 = 0 + 1.875 1.5x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 1.5x + x2 = 1.875 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 = 1.875 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1.875 + 0.5625 Combine like terms: 1.875 + 0.5625 = 2.4375 0.5625 + 1.5x + x2 = 2.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 2.4375 Calculate the square root of the right side: 1.5612495 Break this problem into two subproblems by setting (x + 0.75) equal to 1.5612495 and -1.5612495.Subproblem 1
x + 0.75 = 1.5612495 Simplifying x + 0.75 = 1.5612495 Reorder the terms: 0.75 + x = 1.5612495 Solving 0.75 + x = 1.5612495 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 = 1.5612495 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.5612495 + -0.75 x = 1.5612495 + -0.75 Combine like terms: 1.5612495 + -0.75 = 0.8112495 x = 0.8112495 Simplifying x = 0.8112495Subproblem 2
x + 0.75 = -1.5612495 Simplifying x + 0.75 = -1.5612495 Reorder the terms: 0.75 + x = -1.5612495 Solving 0.75 + x = -1.5612495 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 = -1.5612495 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.5612495 + -0.75 x = -1.5612495 + -0.75 Combine like terms: -1.5612495 + -0.75 = -2.3112495 x = -2.3112495 Simplifying x = -2.3112495Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8112495, -2.3112495}
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