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Simplifying 17x + 12 = 9x2 Reorder the terms: 12 + 17x = 9x2 Solving 12 + 17x = 9x2 Solving for variable 'x'. Combine like terms: 9x2 + -9x2 = 0 12 + 17x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.333333333 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -1.888888889x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -1.888888889x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -1.888888889x + x2 = 0 + 1.333333333 -1.888888889x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -1.888888889x + x2 = 1.333333333 The x term is -1.888888889x. Take half its coefficient (-0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. -1.888888889x + 0.8919753087 + x2 = 1.333333333 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 1.333333333 + 0.8919753087 Combine like terms: 1.333333333 + 0.8919753087 = 2.2253086417 0.8919753087 + -1.888888889x + x2 = 2.2253086417 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 2.2253086417 Calculate the square root of the right side: 1.491746842 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 1.491746842 and -1.491746842.Subproblem 1
x + -0.9444444445 = 1.491746842 Simplifying x + -0.9444444445 = 1.491746842 Reorder the terms: -0.9444444445 + x = 1.491746842 Solving -0.9444444445 + x = 1.491746842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = 1.491746842 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 1.491746842 + 0.9444444445 x = 1.491746842 + 0.9444444445 Combine like terms: 1.491746842 + 0.9444444445 = 2.4361912865 x = 2.4361912865 Simplifying x = 2.4361912865Subproblem 2
x + -0.9444444445 = -1.491746842 Simplifying x + -0.9444444445 = -1.491746842 Reorder the terms: -0.9444444445 + x = -1.491746842 Solving -0.9444444445 + x = -1.491746842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = -1.491746842 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -1.491746842 + 0.9444444445 x = -1.491746842 + 0.9444444445 Combine like terms: -1.491746842 + 0.9444444445 = -0.5473023975 x = -0.5473023975 Simplifying x = -0.5473023975Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4361912865, -0.5473023975}
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