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Simplifying 5x2 + -63x + 72 = 0 Reorder the terms: 72 + -63x + 5x2 = 0 Solving 72 + -63x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 14.4 + -12.6x + x2 = 0 Move the constant term to the right: Add '-14.4' to each side of the equation. 14.4 + -12.6x + -14.4 + x2 = 0 + -14.4 Reorder the terms: 14.4 + -14.4 + -12.6x + x2 = 0 + -14.4 Combine like terms: 14.4 + -14.4 = 0.0 0.0 + -12.6x + x2 = 0 + -14.4 -12.6x + x2 = 0 + -14.4 Combine like terms: 0 + -14.4 = -14.4 -12.6x + x2 = -14.4 The x term is -12.6x. Take half its coefficient (-6.3). Square it (39.69) and add it to both sides. Add '39.69' to each side of the equation. -12.6x + 39.69 + x2 = -14.4 + 39.69 Reorder the terms: 39.69 + -12.6x + x2 = -14.4 + 39.69 Combine like terms: -14.4 + 39.69 = 25.29 39.69 + -12.6x + x2 = 25.29 Factor a perfect square on the left side: (x + -6.3)(x + -6.3) = 25.29 Calculate the square root of the right side: 5.028916384 Break this problem into two subproblems by setting (x + -6.3) equal to 5.028916384 and -5.028916384.Subproblem 1
x + -6.3 = 5.028916384 Simplifying x + -6.3 = 5.028916384 Reorder the terms: -6.3 + x = 5.028916384 Solving -6.3 + x = 5.028916384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.3' to each side of the equation. -6.3 + 6.3 + x = 5.028916384 + 6.3 Combine like terms: -6.3 + 6.3 = 0.0 0.0 + x = 5.028916384 + 6.3 x = 5.028916384 + 6.3 Combine like terms: 5.028916384 + 6.3 = 11.328916384 x = 11.328916384 Simplifying x = 11.328916384Subproblem 2
x + -6.3 = -5.028916384 Simplifying x + -6.3 = -5.028916384 Reorder the terms: -6.3 + x = -5.028916384 Solving -6.3 + x = -5.028916384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.3' to each side of the equation. -6.3 + 6.3 + x = -5.028916384 + 6.3 Combine like terms: -6.3 + 6.3 = 0.0 0.0 + x = -5.028916384 + 6.3 x = -5.028916384 + 6.3 Combine like terms: -5.028916384 + 6.3 = 1.271083616 x = 1.271083616 Simplifying x = 1.271083616Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.328916384, 1.271083616}
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