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Simplifying 15 = 2x(x + -1.5) Reorder the terms: 15 = 2x(-1.5 + x) 15 = (-1.5 * 2x + x * 2x) 15 = (-3x + 2x2) Solving 15 = -3x + 2x2 Solving for variable 'x'. Reorder the terms: 15 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 15 + 3x + -2x2 = 0 + 2x2 + -2x2 15 + 3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 15 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -1.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -1.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -1.5x + x2 = 0 + 7.5 -1.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -1.5x + x2 = 7.5 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 = 7.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 7.5 + 0.5625 Combine like terms: 7.5 + 0.5625 = 8.0625 0.5625 + -1.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -0.75) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -0.75 = 2.839454173 Simplifying x + -0.75 = 2.839454173 Reorder the terms: -0.75 + x = 2.839454173 Solving -0.75 + x = 2.839454173 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 = 2.839454173 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.839454173 + 0.75 x = 2.839454173 + 0.75 Combine like terms: 2.839454173 + 0.75 = 3.589454173 x = 3.589454173 Simplifying x = 3.589454173Subproblem 2
x + -0.75 = -2.839454173 Simplifying x + -0.75 = -2.839454173 Reorder the terms: -0.75 + x = -2.839454173 Solving -0.75 + x = -2.839454173 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 = -2.839454173 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.839454173 + 0.75 x = -2.839454173 + 0.75 Combine like terms: -2.839454173 + 0.75 = -2.089454173 x = -2.089454173 Simplifying x = -2.089454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.589454173, -2.089454173}
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