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Simplifying -2.5x2 + -0.5x + 24 = 0 Reorder the terms: 24 + -0.5x + -2.5x2 = 0 Solving 24 + -0.5x + -2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -9.6 + 0.2x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 0.2x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 0.2x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 0.2x + x2 = 0 + 9.6 0.2x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 0.2x + x2 = 9.6 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 9.6 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 9.6 + 0.01 Combine like terms: 9.6 + 0.01 = 9.61 0.01 + 0.2x + x2 = 9.61 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 9.61 Calculate the square root of the right side: 3.1 Break this problem into two subproblems by setting (x + 0.1) equal to 3.1 and -3.1.Subproblem 1
x + 0.1 = 3.1 Simplifying x + 0.1 = 3.1 Reorder the terms: 0.1 + x = 3.1 Solving 0.1 + x = 3.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 3.1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 3.1 + -0.1 x = 3.1 + -0.1 Combine like terms: 3.1 + -0.1 = 3 x = 3 Simplifying x = 3Subproblem 2
x + 0.1 = -3.1 Simplifying x + 0.1 = -3.1 Reorder the terms: 0.1 + x = -3.1 Solving 0.1 + x = -3.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -3.1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -3.1 + -0.1 x = -3.1 + -0.1 Combine like terms: -3.1 + -0.1 = -3.2 x = -3.2 Simplifying x = -3.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -3.2}
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