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Simplifying 144 + -1x2 + 22.4x = 0 Reorder the terms: 144 + 22.4x + -1x2 = 0 Solving 144 + 22.4x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + -22.4x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + -22.4x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -22.4x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -22.4x + x2 = 0 + 144 -22.4x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -22.4x + x2 = 144 The x term is -22.4x. Take half its coefficient (-11.2). Square it (125.44) and add it to both sides. Add '125.44' to each side of the equation. -22.4x + 125.44 + x2 = 144 + 125.44 Reorder the terms: 125.44 + -22.4x + x2 = 144 + 125.44 Combine like terms: 144 + 125.44 = 269.44 125.44 + -22.4x + x2 = 269.44 Factor a perfect square on the left side: (x + -11.2)(x + -11.2) = 269.44 Calculate the square root of the right side: 16.414627623 Break this problem into two subproblems by setting (x + -11.2) equal to 16.414627623 and -16.414627623.Subproblem 1
x + -11.2 = 16.414627623 Simplifying x + -11.2 = 16.414627623 Reorder the terms: -11.2 + x = 16.414627623 Solving -11.2 + x = 16.414627623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.2' to each side of the equation. -11.2 + 11.2 + x = 16.414627623 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + x = 16.414627623 + 11.2 x = 16.414627623 + 11.2 Combine like terms: 16.414627623 + 11.2 = 27.614627623 x = 27.614627623 Simplifying x = 27.614627623Subproblem 2
x + -11.2 = -16.414627623 Simplifying x + -11.2 = -16.414627623 Reorder the terms: -11.2 + x = -16.414627623 Solving -11.2 + x = -16.414627623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.2' to each side of the equation. -11.2 + 11.2 + x = -16.414627623 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + x = -16.414627623 + 11.2 x = -16.414627623 + 11.2 Combine like terms: -16.414627623 + 11.2 = -5.214627623 x = -5.214627623 Simplifying x = -5.214627623Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.614627623, -5.214627623}
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