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Simplifying 0.013x2 + -1.18x + 28.24 = 4 Reorder the terms: 28.24 + -1.18x + 0.013x2 = 4 Solving 28.24 + -1.18x + 0.013x2 = 4 Solving for variable 'x'. Reorder the terms: 28.24 + -4 + -1.18x + 0.013x2 = 4 + -4 Combine like terms: 28.24 + -4 = 24.24 24.24 + -1.18x + 0.013x2 = 4 + -4 Combine like terms: 4 + -4 = 0 24.24 + -1.18x + 0.013x2 = 0 Begin completing the square. Divide all terms by 0.013 the coefficient of the squared term: Divide each side by '0.013'. 1864.615385 + -90.76923077x + x2 = 0 Move the constant term to the right: Add '-1864.615385' to each side of the equation. 1864.615385 + -90.76923077x + -1864.615385 + x2 = 0 + -1864.615385 Reorder the terms: 1864.615385 + -1864.615385 + -90.76923077x + x2 = 0 + -1864.615385 Combine like terms: 1864.615385 + -1864.615385 = 0.000000 0.000000 + -90.76923077x + x2 = 0 + -1864.615385 -90.76923077x + x2 = 0 + -1864.615385 Combine like terms: 0 + -1864.615385 = -1864.615385 -90.76923077x + x2 = -1864.615385 The x term is -90.76923077x. Take half its coefficient (-45.38461539). Square it (2059.763314) and add it to both sides. Add '2059.763314' to each side of the equation. -90.76923077x + 2059.763314 + x2 = -1864.615385 + 2059.763314 Reorder the terms: 2059.763314 + -90.76923077x + x2 = -1864.615385 + 2059.763314 Combine like terms: -1864.615385 + 2059.763314 = 195.147929 2059.763314 + -90.76923077x + x2 = 195.147929 Factor a perfect square on the left side: (x + -45.38461539)(x + -45.38461539) = 195.147929 Calculate the square root of the right side: 13.969535747 Break this problem into two subproblems by setting (x + -45.38461539) equal to 13.969535747 and -13.969535747.Subproblem 1
x + -45.38461539 = 13.969535747 Simplifying x + -45.38461539 = 13.969535747 Reorder the terms: -45.38461539 + x = 13.969535747 Solving -45.38461539 + x = 13.969535747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.38461539' to each side of the equation. -45.38461539 + 45.38461539 + x = 13.969535747 + 45.38461539 Combine like terms: -45.38461539 + 45.38461539 = 0.00000000 0.00000000 + x = 13.969535747 + 45.38461539 x = 13.969535747 + 45.38461539 Combine like terms: 13.969535747 + 45.38461539 = 59.354151137 x = 59.354151137 Simplifying x = 59.354151137Subproblem 2
x + -45.38461539 = -13.969535747 Simplifying x + -45.38461539 = -13.969535747 Reorder the terms: -45.38461539 + x = -13.969535747 Solving -45.38461539 + x = -13.969535747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.38461539' to each side of the equation. -45.38461539 + 45.38461539 + x = -13.969535747 + 45.38461539 Combine like terms: -45.38461539 + 45.38461539 = 0.00000000 0.00000000 + x = -13.969535747 + 45.38461539 x = -13.969535747 + 45.38461539 Combine like terms: -13.969535747 + 45.38461539 = 31.415079643 x = 31.415079643 Simplifying x = 31.415079643Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.354151137, 31.415079643}
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