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Simplifying 6x2 + 4.5x + -15 = 0 Reorder the terms: -15 + 4.5x + 6x2 = 0 Solving -15 + 4.5x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.75x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.75x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.75x + x2 = 0 + 2.5 0.75x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.75x + x2 = 2.5 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 = 2.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 2.5 + 0.140625 Combine like terms: 2.5 + 0.140625 = 2.640625 0.140625 + 0.75x + x2 = 2.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 2.640625 Calculate the square root of the right side: 1.625 Break this problem into two subproblems by setting (x + 0.375) equal to 1.625 and -1.625.Subproblem 1
x + 0.375 = 1.625 Simplifying x + 0.375 = 1.625 Reorder the terms: 0.375 + x = 1.625 Solving 0.375 + x = 1.625 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 = 1.625 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.625 + -0.375 x = 1.625 + -0.375 Combine like terms: 1.625 + -0.375 = 1.25 x = 1.25 Simplifying x = 1.25Subproblem 2
x + 0.375 = -1.625 Simplifying x + 0.375 = -1.625 Reorder the terms: 0.375 + x = -1.625 Solving 0.375 + x = -1.625 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 = -1.625 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.625 + -0.375 x = -1.625 + -0.375 Combine like terms: -1.625 + -0.375 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.25, -2}
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