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Simplifying 10x2 + -5x + -63 = 6 + 8x Reorder the terms: -63 + -5x + 10x2 = 6 + 8x Solving -63 + -5x + 10x2 = 6 + 8x Solving for variable 'x'. Reorder the terms: -63 + -6 + -5x + -8x + 10x2 = 6 + 8x + -6 + -8x Combine like terms: -63 + -6 = -69 -69 + -5x + -8x + 10x2 = 6 + 8x + -6 + -8x Combine like terms: -5x + -8x = -13x -69 + -13x + 10x2 = 6 + 8x + -6 + -8x Reorder the terms: -69 + -13x + 10x2 = 6 + -6 + 8x + -8x Combine like terms: 6 + -6 = 0 -69 + -13x + 10x2 = 0 + 8x + -8x -69 + -13x + 10x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -69 + -13x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -6.9 + -1.3x + x2 = 0 Move the constant term to the right: Add '6.9' to each side of the equation. -6.9 + -1.3x + 6.9 + x2 = 0 + 6.9 Reorder the terms: -6.9 + 6.9 + -1.3x + x2 = 0 + 6.9 Combine like terms: -6.9 + 6.9 = 0.0 0.0 + -1.3x + x2 = 0 + 6.9 -1.3x + x2 = 0 + 6.9 Combine like terms: 0 + 6.9 = 6.9 -1.3x + x2 = 6.9 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 6.9 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 6.9 + 0.4225 Combine like terms: 6.9 + 0.4225 = 7.3225 0.4225 + -1.3x + x2 = 7.3225 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 7.3225 Calculate the square root of the right side: 2.706011826 Break this problem into two subproblems by setting (x + -0.65) equal to 2.706011826 and -2.706011826.Subproblem 1
x + -0.65 = 2.706011826 Simplifying x + -0.65 = 2.706011826 Reorder the terms: -0.65 + x = 2.706011826 Solving -0.65 + x = 2.706011826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 2.706011826 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 2.706011826 + 0.65 x = 2.706011826 + 0.65 Combine like terms: 2.706011826 + 0.65 = 3.356011826 x = 3.356011826 Simplifying x = 3.356011826Subproblem 2
x + -0.65 = -2.706011826 Simplifying x + -0.65 = -2.706011826 Reorder the terms: -0.65 + x = -2.706011826 Solving -0.65 + x = -2.706011826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -2.706011826 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -2.706011826 + 0.65 x = -2.706011826 + 0.65 Combine like terms: -2.706011826 + 0.65 = -2.056011826 x = -2.056011826 Simplifying x = -2.056011826Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.356011826, -2.056011826}
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