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Simplifying 5x2 = 9x + 17 Reorder the terms: 5x2 = 17 + 9x Solving 5x2 = 17 + 9x Solving for variable 'x'. Reorder the terms: -17 + -9x + 5x2 = 17 + 9x + -17 + -9x Reorder the terms: -17 + -9x + 5x2 = 17 + -17 + 9x + -9x Combine like terms: 17 + -17 = 0 -17 + -9x + 5x2 = 0 + 9x + -9x -17 + -9x + 5x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -17 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + -1.8x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -1.8x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -1.8x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -1.8x + x2 = 0 + 3.4 -1.8x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -1.8x + x2 = 3.4 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 3.4 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 3.4 + 0.81 Combine like terms: 3.4 + 0.81 = 4.21 0.81 + -1.8x + x2 = 4.21 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 4.21 Calculate the square root of the right side: 2.051828453 Break this problem into two subproblems by setting (x + -0.9) equal to 2.051828453 and -2.051828453.Subproblem 1
x + -0.9 = 2.051828453 Simplifying x + -0.9 = 2.051828453 Reorder the terms: -0.9 + x = 2.051828453 Solving -0.9 + x = 2.051828453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 2.051828453 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 2.051828453 + 0.9 x = 2.051828453 + 0.9 Combine like terms: 2.051828453 + 0.9 = 2.951828453 x = 2.951828453 Simplifying x = 2.951828453Subproblem 2
x + -0.9 = -2.051828453 Simplifying x + -0.9 = -2.051828453 Reorder the terms: -0.9 + x = -2.051828453 Solving -0.9 + x = -2.051828453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -2.051828453 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -2.051828453 + 0.9 x = -2.051828453 + 0.9 Combine like terms: -2.051828453 + 0.9 = -1.151828453 x = -1.151828453 Simplifying x = -1.151828453Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.951828453, -1.151828453}
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