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Simplifying 4 = -0.0055x2 + 1.2x + 15 Reorder the terms: 4 = 15 + 1.2x + -0.0055x2 Solving 4 = 15 + 1.2x + -0.0055x2 Solving for variable 'x'. Combine like terms: 4 + -15 = -11 -11 + -1.2x + 0.0055x2 = 15 + 1.2x + -0.0055x2 + -15 + -1.2x + 0.0055x2 Reorder the terms: -11 + -1.2x + 0.0055x2 = 15 + -15 + 1.2x + -1.2x + -0.0055x2 + 0.0055x2 Combine like terms: 15 + -15 = 0 -11 + -1.2x + 0.0055x2 = 0 + 1.2x + -1.2x + -0.0055x2 + 0.0055x2 -11 + -1.2x + 0.0055x2 = 1.2x + -1.2x + -0.0055x2 + 0.0055x2 Combine like terms: 1.2x + -1.2x = 0.0 -11 + -1.2x + 0.0055x2 = 0.0 + -0.0055x2 + 0.0055x2 -11 + -1.2x + 0.0055x2 = -0.0055x2 + 0.0055x2 Combine like terms: -0.0055x2 + 0.0055x2 = 0.0000 -11 + -1.2x + 0.0055x2 = 0.0000 Begin completing the square. Divide all terms by 0.0055 the coefficient of the squared term: Divide each side by '0.0055'. -2000 + -218.1818182x + x2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + -218.1818182x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + -218.1818182x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + -218.1818182x + x2 = 0 + 2000 -218.1818182x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 -218.1818182x + x2 = 2000 The x term is -218.1818182x. Take half its coefficient (-109.0909091). Square it (11900.82645) and add it to both sides. Add '11900.82645' to each side of the equation. -218.1818182x + 11900.82645 + x2 = 2000 + 11900.82645 Reorder the terms: 11900.82645 + -218.1818182x + x2 = 2000 + 11900.82645 Combine like terms: 2000 + 11900.82645 = 13900.82645 11900.82645 + -218.1818182x + x2 = 13900.82645 Factor a perfect square on the left side: (x + -109.0909091)(x + -109.0909091) = 13900.82645 Calculate the square root of the right side: 117.901766102 Break this problem into two subproblems by setting (x + -109.0909091) equal to 117.901766102 and -117.901766102.Subproblem 1
x + -109.0909091 = 117.901766102 Simplifying x + -109.0909091 = 117.901766102 Reorder the terms: -109.0909091 + x = 117.901766102 Solving -109.0909091 + x = 117.901766102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '109.0909091' to each side of the equation. -109.0909091 + 109.0909091 + x = 117.901766102 + 109.0909091 Combine like terms: -109.0909091 + 109.0909091 = 0.0000000 0.0000000 + x = 117.901766102 + 109.0909091 x = 117.901766102 + 109.0909091 Combine like terms: 117.901766102 + 109.0909091 = 226.992675202 x = 226.992675202 Simplifying x = 226.992675202Subproblem 2
x + -109.0909091 = -117.901766102 Simplifying x + -109.0909091 = -117.901766102 Reorder the terms: -109.0909091 + x = -117.901766102 Solving -109.0909091 + x = -117.901766102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '109.0909091' to each side of the equation. -109.0909091 + 109.0909091 + x = -117.901766102 + 109.0909091 Combine like terms: -109.0909091 + 109.0909091 = 0.0000000 0.0000000 + x = -117.901766102 + 109.0909091 x = -117.901766102 + 109.0909091 Combine like terms: -117.901766102 + 109.0909091 = -8.810857002 x = -8.810857002 Simplifying x = -8.810857002Solution
The solution to the problem is based on the solutions from the subproblems. x = {226.992675202, -8.810857002}
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