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Simplifying 2x2 = 9x2 + -72x + 144 Reorder the terms: 2x2 = 144 + -72x + 9x2 Solving 2x2 = 144 + -72x + 9x2 Solving for variable 'x'. Reorder the terms: -144 + 72x + 2x2 + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Combine like terms: 2x2 + -9x2 = -7x2 -144 + 72x + -7x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Reorder the terms: -144 + 72x + -7x2 = 144 + -144 + -72x + 72x + 9x2 + -9x2 Combine like terms: 144 + -144 = 0 -144 + 72x + -7x2 = 0 + -72x + 72x + 9x2 + -9x2 -144 + 72x + -7x2 = -72x + 72x + 9x2 + -9x2 Combine like terms: -72x + 72x = 0 -144 + 72x + -7x2 = 0 + 9x2 + -9x2 -144 + 72x + -7x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -144 + 72x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 20.57142857 + -10.28571429x + x2 = 0 Move the constant term to the right: Add '-20.57142857' to each side of the equation. 20.57142857 + -10.28571429x + -20.57142857 + x2 = 0 + -20.57142857 Reorder the terms: 20.57142857 + -20.57142857 + -10.28571429x + x2 = 0 + -20.57142857 Combine like terms: 20.57142857 + -20.57142857 = 0.00000000 0.00000000 + -10.28571429x + x2 = 0 + -20.57142857 -10.28571429x + x2 = 0 + -20.57142857 Combine like terms: 0 + -20.57142857 = -20.57142857 -10.28571429x + x2 = -20.57142857 The x term is -10.28571429x. Take half its coefficient (-5.142857145). Square it (26.44897961) and add it to both sides. Add '26.44897961' to each side of the equation. -10.28571429x + 26.44897961 + x2 = -20.57142857 + 26.44897961 Reorder the terms: 26.44897961 + -10.28571429x + x2 = -20.57142857 + 26.44897961 Combine like terms: -20.57142857 + 26.44897961 = 5.87755104 26.44897961 + -10.28571429x + x2 = 5.87755104 Factor a perfect square on the left side: (x + -5.142857145)(x + -5.142857145) = 5.87755104 Calculate the square root of the right side: 2.424366111 Break this problem into two subproblems by setting (x + -5.142857145) equal to 2.424366111 and -2.424366111.Subproblem 1
x + -5.142857145 = 2.424366111 Simplifying x + -5.142857145 = 2.424366111 Reorder the terms: -5.142857145 + x = 2.424366111 Solving -5.142857145 + x = 2.424366111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.142857145' to each side of the equation. -5.142857145 + 5.142857145 + x = 2.424366111 + 5.142857145 Combine like terms: -5.142857145 + 5.142857145 = 0.000000000 0.000000000 + x = 2.424366111 + 5.142857145 x = 2.424366111 + 5.142857145 Combine like terms: 2.424366111 + 5.142857145 = 7.567223256 x = 7.567223256 Simplifying x = 7.567223256Subproblem 2
x + -5.142857145 = -2.424366111 Simplifying x + -5.142857145 = -2.424366111 Reorder the terms: -5.142857145 + x = -2.424366111 Solving -5.142857145 + x = -2.424366111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.142857145' to each side of the equation. -5.142857145 + 5.142857145 + x = -2.424366111 + 5.142857145 Combine like terms: -5.142857145 + 5.142857145 = 0.000000000 0.000000000 + x = -2.424366111 + 5.142857145 x = -2.424366111 + 5.142857145 Combine like terms: -2.424366111 + 5.142857145 = 2.718491034 x = 2.718491034 Simplifying x = 2.718491034Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.567223256, 2.718491034}
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