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Simplifying 10x2 + -20 + -8 = 5x2 + -6x Reorder the terms: -20 + -8 + 10x2 = 5x2 + -6x Combine like terms: -20 + -8 = -28 -28 + 10x2 = 5x2 + -6x Reorder the terms: -28 + 10x2 = -6x + 5x2 Solving -28 + 10x2 = -6x + 5x2 Solving for variable 'x'. Reorder the terms: -28 + 6x + 10x2 + -5x2 = -6x + 5x2 + 6x + -5x2 Combine like terms: 10x2 + -5x2 = 5x2 -28 + 6x + 5x2 = -6x + 5x2 + 6x + -5x2 Reorder the terms: -28 + 6x + 5x2 = -6x + 6x + 5x2 + -5x2 Combine like terms: -6x + 6x = 0 -28 + 6x + 5x2 = 0 + 5x2 + -5x2 -28 + 6x + 5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -28 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + 1.2x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 1.2x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 1.2x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 1.2x + x2 = 0 + 5.6 1.2x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 1.2x + x2 = 5.6 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 5.6 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 5.6 + 0.36 Combine like terms: 5.6 + 0.36 = 5.96 0.36 + 1.2x + x2 = 5.96 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 5.96 Calculate the square root of the right side: 2.441311123 Break this problem into two subproblems by setting (x + 0.6) equal to 2.441311123 and -2.441311123.Subproblem 1
x + 0.6 = 2.441311123 Simplifying x + 0.6 = 2.441311123 Reorder the terms: 0.6 + x = 2.441311123 Solving 0.6 + x = 2.441311123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 2.441311123 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 2.441311123 + -0.6 x = 2.441311123 + -0.6 Combine like terms: 2.441311123 + -0.6 = 1.841311123 x = 1.841311123 Simplifying x = 1.841311123Subproblem 2
x + 0.6 = -2.441311123 Simplifying x + 0.6 = -2.441311123 Reorder the terms: 0.6 + x = -2.441311123 Solving 0.6 + x = -2.441311123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -2.441311123 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -2.441311123 + -0.6 x = -2.441311123 + -0.6 Combine like terms: -2.441311123 + -0.6 = -3.041311123 x = -3.041311123 Simplifying x = -3.041311123Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.841311123, -3.041311123}
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