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Simplifying 0.2x2 + -6.7x + -10.5 = 0 Reorder the terms: -10.5 + -6.7x + 0.2x2 = 0 Solving -10.5 + -6.7x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -52.5 + -33.5x + x2 = 0 Move the constant term to the right: Add '52.5' to each side of the equation. -52.5 + -33.5x + 52.5 + x2 = 0 + 52.5 Reorder the terms: -52.5 + 52.5 + -33.5x + x2 = 0 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + -33.5x + x2 = 0 + 52.5 -33.5x + x2 = 0 + 52.5 Combine like terms: 0 + 52.5 = 52.5 -33.5x + x2 = 52.5 The x term is -33.5x. Take half its coefficient (-16.75). Square it (280.5625) and add it to both sides. Add '280.5625' to each side of the equation. -33.5x + 280.5625 + x2 = 52.5 + 280.5625 Reorder the terms: 280.5625 + -33.5x + x2 = 52.5 + 280.5625 Combine like terms: 52.5 + 280.5625 = 333.0625 280.5625 + -33.5x + x2 = 333.0625 Factor a perfect square on the left side: (x + -16.75)(x + -16.75) = 333.0625 Calculate the square root of the right side: 18.25 Break this problem into two subproblems by setting (x + -16.75) equal to 18.25 and -18.25.Subproblem 1
x + -16.75 = 18.25 Simplifying x + -16.75 = 18.25 Reorder the terms: -16.75 + x = 18.25 Solving -16.75 + x = 18.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.75' to each side of the equation. -16.75 + 16.75 + x = 18.25 + 16.75 Combine like terms: -16.75 + 16.75 = 0.00 0.00 + x = 18.25 + 16.75 x = 18.25 + 16.75 Combine like terms: 18.25 + 16.75 = 35 x = 35 Simplifying x = 35Subproblem 2
x + -16.75 = -18.25 Simplifying x + -16.75 = -18.25 Reorder the terms: -16.75 + x = -18.25 Solving -16.75 + x = -18.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.75' to each side of the equation. -16.75 + 16.75 + x = -18.25 + 16.75 Combine like terms: -16.75 + 16.75 = 0.00 0.00 + x = -18.25 + 16.75 x = -18.25 + 16.75 Combine like terms: -18.25 + 16.75 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {35, -1.5}
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