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Simplifying 19.5x2 + -420x + 1600 = 0 Reorder the terms: 1600 + -420x + 19.5x2 = 0 Solving 1600 + -420x + 19.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19.5 the coefficient of the squared term: Divide each side by '19.5'. 82.05128205 + -21.53846154x + x2 = 0 Move the constant term to the right: Add '-82.05128205' to each side of the equation. 82.05128205 + -21.53846154x + -82.05128205 + x2 = 0 + -82.05128205 Reorder the terms: 82.05128205 + -82.05128205 + -21.53846154x + x2 = 0 + -82.05128205 Combine like terms: 82.05128205 + -82.05128205 = 0.00000000 0.00000000 + -21.53846154x + x2 = 0 + -82.05128205 -21.53846154x + x2 = 0 + -82.05128205 Combine like terms: 0 + -82.05128205 = -82.05128205 -21.53846154x + x2 = -82.05128205 The x term is -21.53846154x. Take half its coefficient (-10.76923077). Square it (115.9763314) and add it to both sides. Add '115.9763314' to each side of the equation. -21.53846154x + 115.9763314 + x2 = -82.05128205 + 115.9763314 Reorder the terms: 115.9763314 + -21.53846154x + x2 = -82.05128205 + 115.9763314 Combine like terms: -82.05128205 + 115.9763314 = 33.92504935 115.9763314 + -21.53846154x + x2 = 33.92504935 Factor a perfect square on the left side: (x + -10.76923077)(x + -10.76923077) = 33.92504935 Calculate the square root of the right side: 5.824521384 Break this problem into two subproblems by setting (x + -10.76923077) equal to 5.824521384 and -5.824521384.Subproblem 1
x + -10.76923077 = 5.824521384 Simplifying x + -10.76923077 = 5.824521384 Reorder the terms: -10.76923077 + x = 5.824521384 Solving -10.76923077 + x = 5.824521384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.76923077' to each side of the equation. -10.76923077 + 10.76923077 + x = 5.824521384 + 10.76923077 Combine like terms: -10.76923077 + 10.76923077 = 0.00000000 0.00000000 + x = 5.824521384 + 10.76923077 x = 5.824521384 + 10.76923077 Combine like terms: 5.824521384 + 10.76923077 = 16.593752154 x = 16.593752154 Simplifying x = 16.593752154Subproblem 2
x + -10.76923077 = -5.824521384 Simplifying x + -10.76923077 = -5.824521384 Reorder the terms: -10.76923077 + x = -5.824521384 Solving -10.76923077 + x = -5.824521384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.76923077' to each side of the equation. -10.76923077 + 10.76923077 + x = -5.824521384 + 10.76923077 Combine like terms: -10.76923077 + 10.76923077 = 0.00000000 0.00000000 + x = -5.824521384 + 10.76923077 x = -5.824521384 + 10.76923077 Combine like terms: -5.824521384 + 10.76923077 = 4.944709386 x = 4.944709386 Simplifying x = 4.944709386Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.593752154, 4.944709386}
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