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Simplifying 112.5x2 + -17.64x + -22.05 = 0 Reorder the terms: -22.05 + -17.64x + 112.5x2 = 0 Solving -22.05 + -17.64x + 112.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 112.5 the coefficient of the squared term: Divide each side by '112.5'. -0.196 + -0.1568x + x2 = 0 Move the constant term to the right: Add '0.196' to each side of the equation. -0.196 + -0.1568x + 0.196 + x2 = 0 + 0.196 Reorder the terms: -0.196 + 0.196 + -0.1568x + x2 = 0 + 0.196 Combine like terms: -0.196 + 0.196 = 0.000 0.000 + -0.1568x + x2 = 0 + 0.196 -0.1568x + x2 = 0 + 0.196 Combine like terms: 0 + 0.196 = 0.196 -0.1568x + x2 = 0.196 The x term is -0.1568x. Take half its coefficient (-0.0784). Square it (0.00614656) and add it to both sides. Add '0.00614656' to each side of the equation. -0.1568x + 0.00614656 + x2 = 0.196 + 0.00614656 Reorder the terms: 0.00614656 + -0.1568x + x2 = 0.196 + 0.00614656 Combine like terms: 0.196 + 0.00614656 = 0.20214656 0.00614656 + -0.1568x + x2 = 0.20214656 Factor a perfect square on the left side: (x + -0.0784)(x + -0.0784) = 0.20214656 Calculate the square root of the right side: 0.449607117 Break this problem into two subproblems by setting (x + -0.0784) equal to 0.449607117 and -0.449607117.Subproblem 1
x + -0.0784 = 0.449607117 Simplifying x + -0.0784 = 0.449607117 Reorder the terms: -0.0784 + x = 0.449607117 Solving -0.0784 + x = 0.449607117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0784' to each side of the equation. -0.0784 + 0.0784 + x = 0.449607117 + 0.0784 Combine like terms: -0.0784 + 0.0784 = 0.0000 0.0000 + x = 0.449607117 + 0.0784 x = 0.449607117 + 0.0784 Combine like terms: 0.449607117 + 0.0784 = 0.528007117 x = 0.528007117 Simplifying x = 0.528007117Subproblem 2
x + -0.0784 = -0.449607117 Simplifying x + -0.0784 = -0.449607117 Reorder the terms: -0.0784 + x = -0.449607117 Solving -0.0784 + x = -0.449607117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0784' to each side of the equation. -0.0784 + 0.0784 + x = -0.449607117 + 0.0784 Combine like terms: -0.0784 + 0.0784 = 0.0000 0.0000 + x = -0.449607117 + 0.0784 x = -0.449607117 + 0.0784 Combine like terms: -0.449607117 + 0.0784 = -0.371207117 x = -0.371207117 Simplifying x = -0.371207117Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.528007117, -0.371207117}
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