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Simplifying 10x2 + -3x = 2x2 + 36 Reorder the terms: -3x + 10x2 = 2x2 + 36 Reorder the terms: -3x + 10x2 = 36 + 2x2 Solving -3x + 10x2 = 36 + 2x2 Solving for variable 'x'. Reorder the terms: -36 + -3x + 10x2 + -2x2 = 36 + 2x2 + -36 + -2x2 Combine like terms: 10x2 + -2x2 = 8x2 -36 + -3x + 8x2 = 36 + 2x2 + -36 + -2x2 Reorder the terms: -36 + -3x + 8x2 = 36 + -36 + 2x2 + -2x2 Combine like terms: 36 + -36 = 0 -36 + -3x + 8x2 = 0 + 2x2 + -2x2 -36 + -3x + 8x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -36 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.5 + -0.375x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -0.375x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -0.375x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -0.375x + x2 = 0 + 4.5 -0.375x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -0.375x + x2 = 4.5 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 4.5 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 4.5 + 0.03515625 Combine like terms: 4.5 + 0.03515625 = 4.53515625 0.03515625 + -0.375x + x2 = 4.53515625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 4.53515625 Calculate the square root of the right side: 2.12959063 Break this problem into two subproblems by setting (x + -0.1875) equal to 2.12959063 and -2.12959063.Subproblem 1
x + -0.1875 = 2.12959063 Simplifying x + -0.1875 = 2.12959063 Reorder the terms: -0.1875 + x = 2.12959063 Solving -0.1875 + x = 2.12959063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 2.12959063 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 2.12959063 + 0.1875 x = 2.12959063 + 0.1875 Combine like terms: 2.12959063 + 0.1875 = 2.31709063 x = 2.31709063 Simplifying x = 2.31709063Subproblem 2
x + -0.1875 = -2.12959063 Simplifying x + -0.1875 = -2.12959063 Reorder the terms: -0.1875 + x = -2.12959063 Solving -0.1875 + x = -2.12959063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -2.12959063 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -2.12959063 + 0.1875 x = -2.12959063 + 0.1875 Combine like terms: -2.12959063 + 0.1875 = -1.94209063 x = -1.94209063 Simplifying x = -1.94209063Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.31709063, -1.94209063}
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