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Simplifying 49.4x2 + 33.3x + -63 = 0 Reorder the terms: -63 + 33.3x + 49.4x2 = 0 Solving -63 + 33.3x + 49.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49.4 the coefficient of the squared term: Divide each side by '49.4'. -1.275303644 + 0.6740890688x + x2 = 0 Move the constant term to the right: Add '1.275303644' to each side of the equation. -1.275303644 + 0.6740890688x + 1.275303644 + x2 = 0 + 1.275303644 Reorder the terms: -1.275303644 + 1.275303644 + 0.6740890688x + x2 = 0 + 1.275303644 Combine like terms: -1.275303644 + 1.275303644 = 0.000000000 0.000000000 + 0.6740890688x + x2 = 0 + 1.275303644 0.6740890688x + x2 = 0 + 1.275303644 Combine like terms: 0 + 1.275303644 = 1.275303644 0.6740890688x + x2 = 1.275303644 The x term is 0.6740890688x. Take half its coefficient (0.3370445344). Square it (0.1135990182) and add it to both sides. Add '0.1135990182' to each side of the equation. 0.6740890688x + 0.1135990182 + x2 = 1.275303644 + 0.1135990182 Reorder the terms: 0.1135990182 + 0.6740890688x + x2 = 1.275303644 + 0.1135990182 Combine like terms: 1.275303644 + 0.1135990182 = 1.3889026622 0.1135990182 + 0.6740890688x + x2 = 1.3889026622 Factor a perfect square on the left side: (x + 0.3370445344)(x + 0.3370445344) = 1.3889026622 Calculate the square root of the right side: 1.178517145 Break this problem into two subproblems by setting (x + 0.3370445344) equal to 1.178517145 and -1.178517145.Subproblem 1
x + 0.3370445344 = 1.178517145 Simplifying x + 0.3370445344 = 1.178517145 Reorder the terms: 0.3370445344 + x = 1.178517145 Solving 0.3370445344 + x = 1.178517145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3370445344' to each side of the equation. 0.3370445344 + -0.3370445344 + x = 1.178517145 + -0.3370445344 Combine like terms: 0.3370445344 + -0.3370445344 = 0.0000000000 0.0000000000 + x = 1.178517145 + -0.3370445344 x = 1.178517145 + -0.3370445344 Combine like terms: 1.178517145 + -0.3370445344 = 0.8414726106 x = 0.8414726106 Simplifying x = 0.8414726106Subproblem 2
x + 0.3370445344 = -1.178517145 Simplifying x + 0.3370445344 = -1.178517145 Reorder the terms: 0.3370445344 + x = -1.178517145 Solving 0.3370445344 + x = -1.178517145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3370445344' to each side of the equation. 0.3370445344 + -0.3370445344 + x = -1.178517145 + -0.3370445344 Combine like terms: 0.3370445344 + -0.3370445344 = 0.0000000000 0.0000000000 + x = -1.178517145 + -0.3370445344 x = -1.178517145 + -0.3370445344 Combine like terms: -1.178517145 + -0.3370445344 = -1.5155616794 x = -1.5155616794 Simplifying x = -1.5155616794Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8414726106, -1.5155616794}
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