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Simplifying 0 = 0.2x2 + 3x + -28 Reorder the terms: 0 = -28 + 3x + 0.2x2 Solving 0 = -28 + 3x + 0.2x2 Solving for variable 'x'. Combine like terms: 0 + 28 = 28 28 + -3x + -0.2x2 = -28 + 3x + 0.2x2 + 28 + -3x + -0.2x2 Reorder the terms: 28 + -3x + -0.2x2 = -28 + 28 + 3x + -3x + 0.2x2 + -0.2x2 Combine like terms: -28 + 28 = 0 28 + -3x + -0.2x2 = 0 + 3x + -3x + 0.2x2 + -0.2x2 28 + -3x + -0.2x2 = 3x + -3x + 0.2x2 + -0.2x2 Combine like terms: 3x + -3x = 0 28 + -3x + -0.2x2 = 0 + 0.2x2 + -0.2x2 28 + -3x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 28 + -3x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -140 + 15x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 15x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 15x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 15x + x2 = 0 + 140 15x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 15x + x2 = 140 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 140 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 140 + 56.25 Combine like terms: 140 + 56.25 = 196.25 56.25 + 15x + x2 = 196.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 196.25 Calculate the square root of the right side: 14.008925726 Break this problem into two subproblems by setting (x + 7.5) equal to 14.008925726 and -14.008925726.Subproblem 1
x + 7.5 = 14.008925726 Simplifying x + 7.5 = 14.008925726 Reorder the terms: 7.5 + x = 14.008925726 Solving 7.5 + x = 14.008925726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 14.008925726 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 14.008925726 + -7.5 x = 14.008925726 + -7.5 Combine like terms: 14.008925726 + -7.5 = 6.508925726 x = 6.508925726 Simplifying x = 6.508925726Subproblem 2
x + 7.5 = -14.008925726 Simplifying x + 7.5 = -14.008925726 Reorder the terms: 7.5 + x = -14.008925726 Solving 7.5 + x = -14.008925726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -14.008925726 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -14.008925726 + -7.5 x = -14.008925726 + -7.5 Combine like terms: -14.008925726 + -7.5 = -21.508925726 x = -21.508925726 Simplifying x = -21.508925726Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.508925726, -21.508925726}
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