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Simplifying 34x + -541 = x + -7x2 Reorder the terms: -541 + 34x = x + -7x2 Solving -541 + 34x = x + -7x2 Solving for variable 'x'. Combine like terms: 34x + -1x = 33x -541 + 33x + 7x2 = x + -7x2 + -1x + 7x2 Reorder the terms: -541 + 33x + 7x2 = x + -1x + -7x2 + 7x2 Combine like terms: x + -1x = 0 -541 + 33x + 7x2 = 0 + -7x2 + 7x2 -541 + 33x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -541 + 33x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -77.28571429 + 4.714285714x + x2 = 0 Move the constant term to the right: Add '77.28571429' to each side of the equation. -77.28571429 + 4.714285714x + 77.28571429 + x2 = 0 + 77.28571429 Reorder the terms: -77.28571429 + 77.28571429 + 4.714285714x + x2 = 0 + 77.28571429 Combine like terms: -77.28571429 + 77.28571429 = 0.00000000 0.00000000 + 4.714285714x + x2 = 0 + 77.28571429 4.714285714x + x2 = 0 + 77.28571429 Combine like terms: 0 + 77.28571429 = 77.28571429 4.714285714x + x2 = 77.28571429 The x term is 4.714285714x. Take half its coefficient (2.357142857). Square it (5.556122448) and add it to both sides. Add '5.556122448' to each side of the equation. 4.714285714x + 5.556122448 + x2 = 77.28571429 + 5.556122448 Reorder the terms: 5.556122448 + 4.714285714x + x2 = 77.28571429 + 5.556122448 Combine like terms: 77.28571429 + 5.556122448 = 82.841836738 5.556122448 + 4.714285714x + x2 = 82.841836738 Factor a perfect square on the left side: (x + 2.357142857)(x + 2.357142857) = 82.841836738 Calculate the square root of the right side: 9.101749103 Break this problem into two subproblems by setting (x + 2.357142857) equal to 9.101749103 and -9.101749103.Subproblem 1
x + 2.357142857 = 9.101749103 Simplifying x + 2.357142857 = 9.101749103 Reorder the terms: 2.357142857 + x = 9.101749103 Solving 2.357142857 + x = 9.101749103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.357142857' to each side of the equation. 2.357142857 + -2.357142857 + x = 9.101749103 + -2.357142857 Combine like terms: 2.357142857 + -2.357142857 = 0.000000000 0.000000000 + x = 9.101749103 + -2.357142857 x = 9.101749103 + -2.357142857 Combine like terms: 9.101749103 + -2.357142857 = 6.744606246 x = 6.744606246 Simplifying x = 6.744606246Subproblem 2
x + 2.357142857 = -9.101749103 Simplifying x + 2.357142857 = -9.101749103 Reorder the terms: 2.357142857 + x = -9.101749103 Solving 2.357142857 + x = -9.101749103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.357142857' to each side of the equation. 2.357142857 + -2.357142857 + x = -9.101749103 + -2.357142857 Combine like terms: 2.357142857 + -2.357142857 = 0.000000000 0.000000000 + x = -9.101749103 + -2.357142857 x = -9.101749103 + -2.357142857 Combine like terms: -9.101749103 + -2.357142857 = -11.45889196 x = -11.45889196 Simplifying x = -11.45889196Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.744606246, -11.45889196}
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