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Simplifying 12.5x2 + 15x + 4.5 = 0 Reorder the terms: 4.5 + 15x + 12.5x2 = 0 Solving 4.5 + 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'. 0.36 + 1.2x + x2 = 0 Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + 1.2x + -0.36 + x2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + 1.2x + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + 1.2x + x2 = 0 + -0.36 1.2x + x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 1.2x + x2 = -0.36 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 = -0.36 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.36 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.36 + 1.2x + x2 = 0.00 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 0.6) equal to 0.00 and 0.00.Subproblem 1
x + 0.6 = 0.00 Simplifying x + 0.6 = 0.00 Reorder the terms: 0.6 + x = 0.00 Solving 0.6 + x = 0.00 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 = 0.00 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.00 + -0.6 x = 0.00 + -0.6 Combine like terms: 0.00 + -0.6 = -0.6 x = -0.6 Simplifying x = -0.6Subproblem 2
x + 0.6 = 0.00 Simplifying x + 0.6 = 0.00 Reorder the terms: 0.6 + x = 0.00 Solving 0.6 + x = 0.00 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 = 0.00 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.00 + -0.6 x = 0.00 + -0.6 Combine like terms: 0.00 + -0.6 = -0.6 x = -0.6 Simplifying x = -0.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.6, -0.6}
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