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Simplifying 5x2 + 2x + 3 = 10 + -8x Reorder the terms: 3 + 2x + 5x2 = 10 + -8x Solving 3 + 2x + 5x2 = 10 + -8x Solving for variable 'x'. Reorder the terms: 3 + -10 + 2x + 8x + 5x2 = 10 + -8x + -10 + 8x Combine like terms: 3 + -10 = -7 -7 + 2x + 8x + 5x2 = 10 + -8x + -10 + 8x Combine like terms: 2x + 8x = 10x -7 + 10x + 5x2 = 10 + -8x + -10 + 8x Reorder the terms: -7 + 10x + 5x2 = 10 + -10 + -8x + 8x Combine like terms: 10 + -10 = 0 -7 + 10x + 5x2 = 0 + -8x + 8x -7 + 10x + 5x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -7 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 2x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 2x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 2x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 2x + x2 = 0 + 1.4 2x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 2x + x2 = 1.4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.4 + 1 Reorder the terms: 1 + 2x + x2 = 1.4 + 1 Combine like terms: 1.4 + 1 = 2.4 1 + 2x + x2 = 2.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.4 Calculate the square root of the right side: 1.549193338 Break this problem into two subproblems by setting (x + 1) equal to 1.549193338 and -1.549193338.Subproblem 1
x + 1 = 1.549193338 Simplifying x + 1 = 1.549193338 Reorder the terms: 1 + x = 1.549193338 Solving 1 + x = 1.549193338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.549193338 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.549193338 + -1 x = 1.549193338 + -1 Combine like terms: 1.549193338 + -1 = 0.549193338 x = 0.549193338 Simplifying x = 0.549193338Subproblem 2
x + 1 = -1.549193338 Simplifying x + 1 = -1.549193338 Reorder the terms: 1 + x = -1.549193338 Solving 1 + x = -1.549193338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.549193338 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.549193338 + -1 x = -1.549193338 + -1 Combine like terms: -1.549193338 + -1 = -2.549193338 x = -2.549193338 Simplifying x = -2.549193338Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.549193338, -2.549193338}
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