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Simplifying -0.005x2 + 0.3x + 1.5 = 0 Reorder the terms: 1.5 + 0.3x + -0.005x2 = 0 Solving 1.5 + 0.3x + -0.005x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.005 the coefficient of the squared term: Divide each side by '-0.005'. -300 + -60x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + -60x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -60x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -60x + x2 = 0 + 300 -60x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -60x + x2 = 300 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 300 + 900 Reorder the terms: 900 + -60x + x2 = 300 + 900 Combine like terms: 300 + 900 = 1200 900 + -60x + x2 = 1200 Factor a perfect square on the left side: (x + -30)(x + -30) = 1200 Calculate the square root of the right side: 34.641016151 Break this problem into two subproblems by setting (x + -30) equal to 34.641016151 and -34.641016151.Subproblem 1
x + -30 = 34.641016151 Simplifying x + -30 = 34.641016151 Reorder the terms: -30 + x = 34.641016151 Solving -30 + x = 34.641016151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 34.641016151 + 30 Combine like terms: -30 + 30 = 0 0 + x = 34.641016151 + 30 x = 34.641016151 + 30 Combine like terms: 34.641016151 + 30 = 64.641016151 x = 64.641016151 Simplifying x = 64.641016151Subproblem 2
x + -30 = -34.641016151 Simplifying x + -30 = -34.641016151 Reorder the terms: -30 + x = -34.641016151 Solving -30 + x = -34.641016151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -34.641016151 + 30 Combine like terms: -30 + 30 = 0 0 + x = -34.641016151 + 30 x = -34.641016151 + 30 Combine like terms: -34.641016151 + 30 = -4.641016151 x = -4.641016151 Simplifying x = -4.641016151Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.641016151, -4.641016151}
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