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Simplifying -0.0192x2 + 2.112x + -28.08 = 0 Reorder the terms: -28.08 + 2.112x + -0.0192x2 = 0 Solving -28.08 + 2.112x + -0.0192x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0192 the coefficient of the squared term: Divide each side by '-0.0192'. 1462.5 + -110x + x2 = 0 Move the constant term to the right: Add '-1462.5' to each side of the equation. 1462.5 + -110x + -1462.5 + x2 = 0 + -1462.5 Reorder the terms: 1462.5 + -1462.5 + -110x + x2 = 0 + -1462.5 Combine like terms: 1462.5 + -1462.5 = 0.0 0.0 + -110x + x2 = 0 + -1462.5 -110x + x2 = 0 + -1462.5 Combine like terms: 0 + -1462.5 = -1462.5 -110x + x2 = -1462.5 The x term is -110x. Take half its coefficient (-55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. -110x + 3025 + x2 = -1462.5 + 3025 Reorder the terms: 3025 + -110x + x2 = -1462.5 + 3025 Combine like terms: -1462.5 + 3025 = 1562.5 3025 + -110x + x2 = 1562.5 Factor a perfect square on the left side: (x + -55)(x + -55) = 1562.5 Calculate the square root of the right side: 39.528470752 Break this problem into two subproblems by setting (x + -55) equal to 39.528470752 and -39.528470752.Subproblem 1
x + -55 = 39.528470752 Simplifying x + -55 = 39.528470752 Reorder the terms: -55 + x = 39.528470752 Solving -55 + x = 39.528470752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = 39.528470752 + 55 Combine like terms: -55 + 55 = 0 0 + x = 39.528470752 + 55 x = 39.528470752 + 55 Combine like terms: 39.528470752 + 55 = 94.528470752 x = 94.528470752 Simplifying x = 94.528470752Subproblem 2
x + -55 = -39.528470752 Simplifying x + -55 = -39.528470752 Reorder the terms: -55 + x = -39.528470752 Solving -55 + x = -39.528470752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = -39.528470752 + 55 Combine like terms: -55 + 55 = 0 0 + x = -39.528470752 + 55 x = -39.528470752 + 55 Combine like terms: -39.528470752 + 55 = 15.471529248 x = 15.471529248 Simplifying x = 15.471529248Solution
The solution to the problem is based on the solutions from the subproblems. x = {94.528470752, 15.471529248}
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