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Simplifying 9 = -0.1x2 + -0.2x + 57 Reorder the terms: 9 = 57 + -0.2x + -0.1x2 Solving 9 = 57 + -0.2x + -0.1x2 Solving for variable 'x'. Combine like terms: 9 + -57 = -48 -48 + 0.2x + 0.1x2 = 57 + -0.2x + -0.1x2 + -57 + 0.2x + 0.1x2 Reorder the terms: -48 + 0.2x + 0.1x2 = 57 + -57 + -0.2x + 0.2x + -0.1x2 + 0.1x2 Combine like terms: 57 + -57 = 0 -48 + 0.2x + 0.1x2 = 0 + -0.2x + 0.2x + -0.1x2 + 0.1x2 -48 + 0.2x + 0.1x2 = -0.2x + 0.2x + -0.1x2 + 0.1x2 Combine like terms: -0.2x + 0.2x = 0.0 -48 + 0.2x + 0.1x2 = 0.0 + -0.1x2 + 0.1x2 -48 + 0.2x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 -48 + 0.2x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -480 + 2x + x2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + 2x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 2x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 2x + x2 = 0 + 480 2x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 2x + x2 = 480 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 480 + 1 Reorder the terms: 1 + 2x + x2 = 480 + 1 Combine like terms: 480 + 1 = 481 1 + 2x + x2 = 481 Factor a perfect square on the left side: (x + 1)(x + 1) = 481 Calculate the square root of the right side: 21.931712199 Break this problem into two subproblems by setting (x + 1) equal to 21.931712199 and -21.931712199.Subproblem 1
x + 1 = 21.931712199 Simplifying x + 1 = 21.931712199 Reorder the terms: 1 + x = 21.931712199 Solving 1 + x = 21.931712199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 21.931712199 + -1 Combine like terms: 1 + -1 = 0 0 + x = 21.931712199 + -1 x = 21.931712199 + -1 Combine like terms: 21.931712199 + -1 = 20.931712199 x = 20.931712199 Simplifying x = 20.931712199Subproblem 2
x + 1 = -21.931712199 Simplifying x + 1 = -21.931712199 Reorder the terms: 1 + x = -21.931712199 Solving 1 + x = -21.931712199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -21.931712199 + -1 Combine like terms: 1 + -1 = 0 0 + x = -21.931712199 + -1 x = -21.931712199 + -1 Combine like terms: -21.931712199 + -1 = -22.931712199 x = -22.931712199 Simplifying x = -22.931712199Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.931712199, -22.931712199}
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