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Simplifying 8.3x2 + -2x + -74.7 = 0 Reorder the terms: -74.7 + -2x + 8.3x2 = 0 Solving -74.7 + -2x + 8.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.3 the coefficient of the squared term: Divide each side by '8.3'. -9 + -0.2409638554x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.2409638554x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.2409638554x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.2409638554x + x2 = 0 + 9 -0.2409638554x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.2409638554x + x2 = 9 The x term is -0.2409638554x. Take half its coefficient (-0.1204819277). Square it (0.01451589490) and add it to both sides. Add '0.01451589490' to each side of the equation. -0.2409638554x + 0.01451589490 + x2 = 9 + 0.01451589490 Reorder the terms: 0.01451589490 + -0.2409638554x + x2 = 9 + 0.01451589490 Combine like terms: 9 + 0.01451589490 = 9.0145158949 0.01451589490 + -0.2409638554x + x2 = 9.0145158949 Factor a perfect square on the left side: (x + -0.1204819277)(x + -0.1204819277) = 9.0145158949 Calculate the square root of the right side: 3.002418341 Break this problem into two subproblems by setting (x + -0.1204819277) equal to 3.002418341 and -3.002418341.Subproblem 1
x + -0.1204819277 = 3.002418341 Simplifying x + -0.1204819277 = 3.002418341 Reorder the terms: -0.1204819277 + x = 3.002418341 Solving -0.1204819277 + x = 3.002418341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1204819277' to each side of the equation. -0.1204819277 + 0.1204819277 + x = 3.002418341 + 0.1204819277 Combine like terms: -0.1204819277 + 0.1204819277 = 0.0000000000 0.0000000000 + x = 3.002418341 + 0.1204819277 x = 3.002418341 + 0.1204819277 Combine like terms: 3.002418341 + 0.1204819277 = 3.1229002687 x = 3.1229002687 Simplifying x = 3.1229002687Subproblem 2
x + -0.1204819277 = -3.002418341 Simplifying x + -0.1204819277 = -3.002418341 Reorder the terms: -0.1204819277 + x = -3.002418341 Solving -0.1204819277 + x = -3.002418341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1204819277' to each side of the equation. -0.1204819277 + 0.1204819277 + x = -3.002418341 + 0.1204819277 Combine like terms: -0.1204819277 + 0.1204819277 = 0.0000000000 0.0000000000 + x = -3.002418341 + 0.1204819277 x = -3.002418341 + 0.1204819277 Combine like terms: -3.002418341 + 0.1204819277 = -2.8819364133 x = -2.8819364133 Simplifying x = -2.8819364133Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1229002687, -2.8819364133}
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