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Simplifying 3x2 + 21x + -32 = 2x2 + 10 Reorder the terms: -32 + 21x + 3x2 = 2x2 + 10 Reorder the terms: -32 + 21x + 3x2 = 10 + 2x2 Solving -32 + 21x + 3x2 = 10 + 2x2 Solving for variable 'x'. Reorder the terms: -32 + -10 + 21x + 3x2 + -2x2 = 10 + 2x2 + -10 + -2x2 Combine like terms: -32 + -10 = -42 -42 + 21x + 3x2 + -2x2 = 10 + 2x2 + -10 + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -42 + 21x + 1x2 = 10 + 2x2 + -10 + -2x2 Reorder the terms: -42 + 21x + 1x2 = 10 + -10 + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 -42 + 21x + 1x2 = 0 + 2x2 + -2x2 -42 + 21x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -42 + 21x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 21x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 21x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 21x + x2 = 0 + 42 21x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 21x + x2 = 42 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 42 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 42 + 110.25 Combine like terms: 42 + 110.25 = 152.25 110.25 + 21x + x2 = 152.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 152.25 Calculate the square root of the right side: 12.338962679 Break this problem into two subproblems by setting (x + 10.5) equal to 12.338962679 and -12.338962679.Subproblem 1
x + 10.5 = 12.338962679 Simplifying x + 10.5 = 12.338962679 Reorder the terms: 10.5 + x = 12.338962679 Solving 10.5 + x = 12.338962679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 12.338962679 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 12.338962679 + -10.5 x = 12.338962679 + -10.5 Combine like terms: 12.338962679 + -10.5 = 1.838962679 x = 1.838962679 Simplifying x = 1.838962679Subproblem 2
x + 10.5 = -12.338962679 Simplifying x + 10.5 = -12.338962679 Reorder the terms: 10.5 + x = -12.338962679 Solving 10.5 + x = -12.338962679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -12.338962679 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -12.338962679 + -10.5 x = -12.338962679 + -10.5 Combine like terms: -12.338962679 + -10.5 = -22.838962679 x = -22.838962679 Simplifying x = -22.838962679Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.838962679, -22.838962679}
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