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Simplifying 5x2 + -9x = 9 Reorder the terms: -9x + 5x2 = 9 Solving -9x + 5x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -9x + 5x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -1.8x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -1.8x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -1.8x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -1.8x + x2 = 0 + 1.8 -1.8x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -1.8x + x2 = 1.8 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 = 1.8 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 1.8 + 0.81 Combine like terms: 1.8 + 0.81 = 2.61 0.81 + -1.8x + x2 = 2.61 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 2.61 Calculate the square root of the right side: 1.615549442 Break this problem into two subproblems by setting (x + -0.9) equal to 1.615549442 and -1.615549442.Subproblem 1
x + -0.9 = 1.615549442 Simplifying x + -0.9 = 1.615549442 Reorder the terms: -0.9 + x = 1.615549442 Solving -0.9 + x = 1.615549442 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 = 1.615549442 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.615549442 + 0.9 x = 1.615549442 + 0.9 Combine like terms: 1.615549442 + 0.9 = 2.515549442 x = 2.515549442 Simplifying x = 2.515549442Subproblem 2
x + -0.9 = -1.615549442 Simplifying x + -0.9 = -1.615549442 Reorder the terms: -0.9 + x = -1.615549442 Solving -0.9 + x = -1.615549442 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 = -1.615549442 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.615549442 + 0.9 x = -1.615549442 + 0.9 Combine like terms: -1.615549442 + 0.9 = -0.715549442 x = -0.715549442 Simplifying x = -0.715549442Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.515549442, -0.715549442}
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