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Simplifying 12.5x2 + 15x + 0.5 = 0 Reorder the terms: 0.5 + 15x + 12.5x2 = 0 Solving 0.5 + 15x + 12.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12.5 the coefficient of the squared term: Divide each side by '12.5'. 0.04 + 1.2x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 1.2x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 1.2x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 1.2x + x2 = 0 + -0.04 1.2x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 1.2x + x2 = -0.04 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = -0.04 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.04 + 0.36 Combine like terms: -0.04 + 0.36 = 0.32 0.36 + 1.2x + x2 = 0.32 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.32 Calculate the square root of the right side: 0.565685425 Break this problem into two subproblems by setting (x + 0.6) equal to 0.565685425 and -0.565685425.Subproblem 1
x + 0.6 = 0.565685425 Simplifying x + 0.6 = 0.565685425 Reorder the terms: 0.6 + x = 0.565685425 Solving 0.6 + x = 0.565685425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.565685425 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.565685425 + -0.6 x = 0.565685425 + -0.6 Combine like terms: 0.565685425 + -0.6 = -0.034314575 x = -0.034314575 Simplifying x = -0.034314575Subproblem 2
x + 0.6 = -0.565685425 Simplifying x + 0.6 = -0.565685425 Reorder the terms: 0.6 + x = -0.565685425 Solving 0.6 + x = -0.565685425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.565685425 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.565685425 + -0.6 x = -0.565685425 + -0.6 Combine like terms: -0.565685425 + -0.6 = -1.165685425 x = -1.165685425 Simplifying x = -1.165685425Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.034314575, -1.165685425}
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