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Simplifying 0 = -42.24x2 + 24x + 3 Reorder the terms: 0 = 3 + 24x + -42.24x2 Solving 0 = 3 + 24x + -42.24x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -24x + 42.24x2 = 3 + 24x + -42.24x2 + -3 + -24x + 42.24x2 Reorder the terms: -3 + -24x + 42.24x2 = 3 + -3 + 24x + -24x + -42.24x2 + 42.24x2 Combine like terms: 3 + -3 = 0 -3 + -24x + 42.24x2 = 0 + 24x + -24x + -42.24x2 + 42.24x2 -3 + -24x + 42.24x2 = 24x + -24x + -42.24x2 + 42.24x2 Combine like terms: 24x + -24x = 0 -3 + -24x + 42.24x2 = 0 + -42.24x2 + 42.24x2 -3 + -24x + 42.24x2 = -42.24x2 + 42.24x2 Combine like terms: -42.24x2 + 42.24x2 = 0.00 -3 + -24x + 42.24x2 = 0.00 Begin completing the square. Divide all terms by 42.24 the coefficient of the squared term: Divide each side by '42.24'. -0.07102272727 + -0.5681818182x + x2 = 0 Move the constant term to the right: Add '0.07102272727' to each side of the equation. -0.07102272727 + -0.5681818182x + 0.07102272727 + x2 = 0 + 0.07102272727 Reorder the terms: -0.07102272727 + 0.07102272727 + -0.5681818182x + x2 = 0 + 0.07102272727 Combine like terms: -0.07102272727 + 0.07102272727 = 0.00000000000 0.00000000000 + -0.5681818182x + x2 = 0 + 0.07102272727 -0.5681818182x + x2 = 0 + 0.07102272727 Combine like terms: 0 + 0.07102272727 = 0.07102272727 -0.5681818182x + x2 = 0.07102272727 The x term is -0.5681818182x. Take half its coefficient (-0.2840909091). Square it (0.08070764463) and add it to both sides. Add '0.08070764463' to each side of the equation. -0.5681818182x + 0.08070764463 + x2 = 0.07102272727 + 0.08070764463 Reorder the terms: 0.08070764463 + -0.5681818182x + x2 = 0.07102272727 + 0.08070764463 Combine like terms: 0.07102272727 + 0.08070764463 = 0.1517303719 0.08070764463 + -0.5681818182x + x2 = 0.1517303719 Factor a perfect square on the left side: (x + -0.2840909091)(x + -0.2840909091) = 0.1517303719 Calculate the square root of the right side: 0.38952583 Break this problem into two subproblems by setting (x + -0.2840909091) equal to 0.38952583 and -0.38952583.Subproblem 1
x + -0.2840909091 = 0.38952583 Simplifying x + -0.2840909091 = 0.38952583 Reorder the terms: -0.2840909091 + x = 0.38952583 Solving -0.2840909091 + x = 0.38952583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2840909091' to each side of the equation. -0.2840909091 + 0.2840909091 + x = 0.38952583 + 0.2840909091 Combine like terms: -0.2840909091 + 0.2840909091 = 0.0000000000 0.0000000000 + x = 0.38952583 + 0.2840909091 x = 0.38952583 + 0.2840909091 Combine like terms: 0.38952583 + 0.2840909091 = 0.6736167391 x = 0.6736167391 Simplifying x = 0.6736167391Subproblem 2
x + -0.2840909091 = -0.38952583 Simplifying x + -0.2840909091 = -0.38952583 Reorder the terms: -0.2840909091 + x = -0.38952583 Solving -0.2840909091 + x = -0.38952583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2840909091' to each side of the equation. -0.2840909091 + 0.2840909091 + x = -0.38952583 + 0.2840909091 Combine like terms: -0.2840909091 + 0.2840909091 = 0.0000000000 0.0000000000 + x = -0.38952583 + 0.2840909091 x = -0.38952583 + 0.2840909091 Combine like terms: -0.38952583 + 0.2840909091 = -0.1054349209 x = -0.1054349209 Simplifying x = -0.1054349209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6736167391, -0.1054349209}
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