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Simplifying 5x2 + 15x + 0.5 = 0 Reorder the terms: 0.5 + 15x + 5x2 = 0 Solving 0.5 + 15x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.1 + 3x + x2 = 0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 3x + -0.1 + x2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + 3x + x2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 3x + x2 = 0 + -0.1 3x + x2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 3x + x2 = -0.1 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -0.1 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.1 + 2.25 Combine like terms: -0.1 + 2.25 = 2.15 2.25 + 3x + x2 = 2.15 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.15 Calculate the square root of the right side: 1.46628783 Break this problem into two subproblems by setting (x + 1.5) equal to 1.46628783 and -1.46628783.Subproblem 1
x + 1.5 = 1.46628783 Simplifying x + 1.5 = 1.46628783 Reorder the terms: 1.5 + x = 1.46628783 Solving 1.5 + x = 1.46628783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.46628783 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.46628783 + -1.5 x = 1.46628783 + -1.5 Combine like terms: 1.46628783 + -1.5 = -0.03371217 x = -0.03371217 Simplifying x = -0.03371217Subproblem 2
x + 1.5 = -1.46628783 Simplifying x + 1.5 = -1.46628783 Reorder the terms: 1.5 + x = -1.46628783 Solving 1.5 + x = -1.46628783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.46628783 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.46628783 + -1.5 x = -1.46628783 + -1.5 Combine like terms: -1.46628783 + -1.5 = -2.96628783 x = -2.96628783 Simplifying x = -2.96628783Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.03371217, -2.96628783}
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