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Simplifying 1.5 = -0.00009x2 + 0.0287x + 1.2959 Reorder the terms: 1.5 = 1.2959 + 0.0287x + -0.00009x2 Solving 1.5 = 1.2959 + 0.0287x + -0.00009x2 Solving for variable 'x'. Combine like terms: 1.5 + -1.2959 = 0.2041 0.2041 + -0.0287x + 0.00009x2 = 1.2959 + 0.0287x + -0.00009x2 + -1.2959 + -0.0287x + 0.00009x2 Reorder the terms: 0.2041 + -0.0287x + 0.00009x2 = 1.2959 + -1.2959 + 0.0287x + -0.0287x + -0.00009x2 + 0.00009x2 Combine like terms: 1.2959 + -1.2959 = 0.0000 0.2041 + -0.0287x + 0.00009x2 = 0.0000 + 0.0287x + -0.0287x + -0.00009x2 + 0.00009x2 0.2041 + -0.0287x + 0.00009x2 = 0.0287x + -0.0287x + -0.00009x2 + 0.00009x2 Combine like terms: 0.0287x + -0.0287x = 0.0000 0.2041 + -0.0287x + 0.00009x2 = 0.0000 + -0.00009x2 + 0.00009x2 0.2041 + -0.0287x + 0.00009x2 = -0.00009x2 + 0.00009x2 Combine like terms: -0.00009x2 + 0.00009x2 = 0.00000 0.2041 + -0.0287x + 0.00009x2 = 0.00000 Begin completing the square. Divide all terms by 0.00009 the coefficient of the squared term: Divide each side by '0.00009'. 2267.777778 + -318.8888889x + x2 = 0 Move the constant term to the right: Add '-2267.777778' to each side of the equation. 2267.777778 + -318.8888889x + -2267.777778 + x2 = 0 + -2267.777778 Reorder the terms: 2267.777778 + -2267.777778 + -318.8888889x + x2 = 0 + -2267.777778 Combine like terms: 2267.777778 + -2267.777778 = 0.000000 0.000000 + -318.8888889x + x2 = 0 + -2267.777778 -318.8888889x + x2 = 0 + -2267.777778 Combine like terms: 0 + -2267.777778 = -2267.777778 -318.8888889x + x2 = -2267.777778 The x term is -318.8888889x. Take half its coefficient (-159.4444445). Square it (25422.53088) and add it to both sides. Add '25422.53088' to each side of the equation. -318.8888889x + 25422.53088 + x2 = -2267.777778 + 25422.53088 Reorder the terms: 25422.53088 + -318.8888889x + x2 = -2267.777778 + 25422.53088 Combine like terms: -2267.777778 + 25422.53088 = 23154.753102 25422.53088 + -318.8888889x + x2 = 23154.753102 Factor a perfect square on the left side: (x + -159.4444445)(x + -159.4444445) = 23154.753102 Calculate the square root of the right side: 152.166859408 Break this problem into two subproblems by setting (x + -159.4444445) equal to 152.166859408 and -152.166859408.Subproblem 1
x + -159.4444445 = 152.166859408 Simplifying x + -159.4444445 = 152.166859408 Reorder the terms: -159.4444445 + x = 152.166859408 Solving -159.4444445 + x = 152.166859408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '159.4444445' to each side of the equation. -159.4444445 + 159.4444445 + x = 152.166859408 + 159.4444445 Combine like terms: -159.4444445 + 159.4444445 = 0.0000000 0.0000000 + x = 152.166859408 + 159.4444445 x = 152.166859408 + 159.4444445 Combine like terms: 152.166859408 + 159.4444445 = 311.611303908 x = 311.611303908 Simplifying x = 311.611303908Subproblem 2
x + -159.4444445 = -152.166859408 Simplifying x + -159.4444445 = -152.166859408 Reorder the terms: -159.4444445 + x = -152.166859408 Solving -159.4444445 + x = -152.166859408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '159.4444445' to each side of the equation. -159.4444445 + 159.4444445 + x = -152.166859408 + 159.4444445 Combine like terms: -159.4444445 + 159.4444445 = 0.0000000 0.0000000 + x = -152.166859408 + 159.4444445 x = -152.166859408 + 159.4444445 Combine like terms: -152.166859408 + 159.4444445 = 7.277585092 x = 7.277585092 Simplifying x = 7.277585092Solution
The solution to the problem is based on the solutions from the subproblems. x = {311.611303908, 7.277585092}
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