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Simplifying -0.02x2 + 1.2x + 6.3 = 0 Reorder the terms: 6.3 + 1.2x + -0.02x2 = 0 Solving 6.3 + 1.2x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. -315 + -60x + x2 = 0 Move the constant term to the right: Add '315' to each side of the equation. -315 + -60x + 315 + x2 = 0 + 315 Reorder the terms: -315 + 315 + -60x + x2 = 0 + 315 Combine like terms: -315 + 315 = 0 0 + -60x + x2 = 0 + 315 -60x + x2 = 0 + 315 Combine like terms: 0 + 315 = 315 -60x + x2 = 315 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 = 315 + 900 Reorder the terms: 900 + -60x + x2 = 315 + 900 Combine like terms: 315 + 900 = 1215 900 + -60x + x2 = 1215 Factor a perfect square on the left side: (x + -30)(x + -30) = 1215 Calculate the square root of the right side: 34.856850116 Break this problem into two subproblems by setting (x + -30) equal to 34.856850116 and -34.856850116.Subproblem 1
x + -30 = 34.856850116 Simplifying x + -30 = 34.856850116 Reorder the terms: -30 + x = 34.856850116 Solving -30 + x = 34.856850116 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 = 34.856850116 + 30 Combine like terms: -30 + 30 = 0 0 + x = 34.856850116 + 30 x = 34.856850116 + 30 Combine like terms: 34.856850116 + 30 = 64.856850116 x = 64.856850116 Simplifying x = 64.856850116Subproblem 2
x + -30 = -34.856850116 Simplifying x + -30 = -34.856850116 Reorder the terms: -30 + x = -34.856850116 Solving -30 + x = -34.856850116 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 = -34.856850116 + 30 Combine like terms: -30 + 30 = 0 0 + x = -34.856850116 + 30 x = -34.856850116 + 30 Combine like terms: -34.856850116 + 30 = -4.856850116 x = -4.856850116 Simplifying x = -4.856850116Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.856850116, -4.856850116}
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