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Simplifying 10x2 + 2.784x = 27.84 Reorder the terms: 2.784x + 10x2 = 27.84 Solving 2.784x + 10x2 = 27.84 Solving for variable 'x'. Reorder the terms: -27.84 + 2.784x + 10x2 = 27.84 + -27.84 Combine like terms: 27.84 + -27.84 = 0.00 -27.84 + 2.784x + 10x2 = 0.00 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.784 + 0.2784x + x2 = 0.00 Move the constant term to the right: Add '2.784' to each side of the equation. -2.784 + 0.2784x + 2.784 + x2 = 0.00 + 2.784 Reorder the terms: -2.784 + 2.784 + 0.2784x + x2 = 0.00 + 2.784 Combine like terms: -2.784 + 2.784 = 0.000 0.000 + 0.2784x + x2 = 0.00 + 2.784 0.2784x + x2 = 0.00 + 2.784 Combine like terms: 0.00 + 2.784 = 2.784 0.2784x + x2 = 2.784 The x term is 0.2784x. Take half its coefficient (0.1392). Square it (0.01937664) and add it to both sides. Add '0.01937664' to each side of the equation. 0.2784x + 0.01937664 + x2 = 2.784 + 0.01937664 Reorder the terms: 0.01937664 + 0.2784x + x2 = 2.784 + 0.01937664 Combine like terms: 2.784 + 0.01937664 = 2.80337664 0.01937664 + 0.2784x + x2 = 2.80337664 Factor a perfect square on the left side: (x + 0.1392)(x + 0.1392) = 2.80337664 Calculate the square root of the right side: 1.674328713 Break this problem into two subproblems by setting (x + 0.1392) equal to 1.674328713 and -1.674328713.Subproblem 1
x + 0.1392 = 1.674328713 Simplifying x + 0.1392 = 1.674328713 Reorder the terms: 0.1392 + x = 1.674328713 Solving 0.1392 + x = 1.674328713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1392' to each side of the equation. 0.1392 + -0.1392 + x = 1.674328713 + -0.1392 Combine like terms: 0.1392 + -0.1392 = 0.0000 0.0000 + x = 1.674328713 + -0.1392 x = 1.674328713 + -0.1392 Combine like terms: 1.674328713 + -0.1392 = 1.535128713 x = 1.535128713 Simplifying x = 1.535128713Subproblem 2
x + 0.1392 = -1.674328713 Simplifying x + 0.1392 = -1.674328713 Reorder the terms: 0.1392 + x = -1.674328713 Solving 0.1392 + x = -1.674328713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1392' to each side of the equation. 0.1392 + -0.1392 + x = -1.674328713 + -0.1392 Combine like terms: 0.1392 + -0.1392 = 0.0000 0.0000 + x = -1.674328713 + -0.1392 x = -1.674328713 + -0.1392 Combine like terms: -1.674328713 + -0.1392 = -1.813528713 x = -1.813528713 Simplifying x = -1.813528713Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.535128713, -1.813528713}
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