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Simplifying 77 = 36x + -1(0.2x2) + -90 Remove parenthesis around (0.2x2) 77 = 36x + -1 * 0.2x2 + -90 Multiply -1 * 0.2 77 = 36x + -0.2x2 + -90 Reorder the terms: 77 = -90 + 36x + -0.2x2 Solving 77 = -90 + 36x + -0.2x2 Solving for variable 'x'. Combine like terms: 77 + 90 = 167 167 + -36x + 0.2x2 = -90 + 36x + -0.2x2 + 90 + -36x + 0.2x2 Reorder the terms: 167 + -36x + 0.2x2 = -90 + 90 + 36x + -36x + -0.2x2 + 0.2x2 Combine like terms: -90 + 90 = 0 167 + -36x + 0.2x2 = 0 + 36x + -36x + -0.2x2 + 0.2x2 167 + -36x + 0.2x2 = 36x + -36x + -0.2x2 + 0.2x2 Combine like terms: 36x + -36x = 0 167 + -36x + 0.2x2 = 0 + -0.2x2 + 0.2x2 167 + -36x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 167 + -36x + 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'. 835 + -180x + x2 = 0 Move the constant term to the right: Add '-835' to each side of the equation. 835 + -180x + -835 + x2 = 0 + -835 Reorder the terms: 835 + -835 + -180x + x2 = 0 + -835 Combine like terms: 835 + -835 = 0 0 + -180x + x2 = 0 + -835 -180x + x2 = 0 + -835 Combine like terms: 0 + -835 = -835 -180x + x2 = -835 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -835 + 8100 Reorder the terms: 8100 + -180x + x2 = -835 + 8100 Combine like terms: -835 + 8100 = 7265 8100 + -180x + x2 = 7265 Factor a perfect square on the left side: (x + -90)(x + -90) = 7265 Calculate the square root of the right side: 85.234969349 Break this problem into two subproblems by setting (x + -90) equal to 85.234969349 and -85.234969349.Subproblem 1
x + -90 = 85.234969349 Simplifying x + -90 = 85.234969349 Reorder the terms: -90 + x = 85.234969349 Solving -90 + x = 85.234969349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 85.234969349 + 90 Combine like terms: -90 + 90 = 0 0 + x = 85.234969349 + 90 x = 85.234969349 + 90 Combine like terms: 85.234969349 + 90 = 175.234969349 x = 175.234969349 Simplifying x = 175.234969349Subproblem 2
x + -90 = -85.234969349 Simplifying x + -90 = -85.234969349 Reorder the terms: -90 + x = -85.234969349 Solving -90 + x = -85.234969349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -85.234969349 + 90 Combine like terms: -90 + 90 = 0 0 + x = -85.234969349 + 90 x = -85.234969349 + 90 Combine like terms: -85.234969349 + 90 = 4.765030651 x = 4.765030651 Simplifying x = 4.765030651Solution
The solution to the problem is based on the solutions from the subproblems. x = {175.234969349, 4.765030651}
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