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Simplifying 5x2 + -2x = 7x + 8 Reorder the terms: -2x + 5x2 = 7x + 8 Reorder the terms: -2x + 5x2 = 8 + 7x Solving -2x + 5x2 = 8 + 7x Solving for variable 'x'. Reorder the terms: -8 + -2x + -7x + 5x2 = 8 + 7x + -8 + -7x Combine like terms: -2x + -7x = -9x -8 + -9x + 5x2 = 8 + 7x + -8 + -7x Reorder the terms: -8 + -9x + 5x2 = 8 + -8 + 7x + -7x Combine like terms: 8 + -8 = 0 -8 + -9x + 5x2 = 0 + 7x + -7x -8 + -9x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -8 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -1.8x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -1.8x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -1.8x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -1.8x + x2 = 0 + 1.6 -1.8x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -1.8x + x2 = 1.6 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 = 1.6 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 1.6 + 0.81 Combine like terms: 1.6 + 0.81 = 2.41 0.81 + -1.8x + x2 = 2.41 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (x + -0.9) equal to 1.55241747 and -1.55241747.Subproblem 1
x + -0.9 = 1.55241747 Simplifying x + -0.9 = 1.55241747 Reorder the terms: -0.9 + x = 1.55241747 Solving -0.9 + x = 1.55241747 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 = 1.55241747 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.55241747 + 0.9 x = 1.55241747 + 0.9 Combine like terms: 1.55241747 + 0.9 = 2.45241747 x = 2.45241747 Simplifying x = 2.45241747Subproblem 2
x + -0.9 = -1.55241747 Simplifying x + -0.9 = -1.55241747 Reorder the terms: -0.9 + x = -1.55241747 Solving -0.9 + x = -1.55241747 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 = -1.55241747 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.55241747 + 0.9 x = -1.55241747 + 0.9 Combine like terms: -1.55241747 + 0.9 = -0.65241747 x = -0.65241747 Simplifying x = -0.65241747Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.45241747, -0.65241747}
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