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Simplifying 5x2 + -3x + 10 = 2x2 + 21 Reorder the terms: 10 + -3x + 5x2 = 2x2 + 21 Reorder the terms: 10 + -3x + 5x2 = 21 + 2x2 Solving 10 + -3x + 5x2 = 21 + 2x2 Solving for variable 'x'. Reorder the terms: 10 + -21 + -3x + 5x2 + -2x2 = 21 + 2x2 + -21 + -2x2 Combine like terms: 10 + -21 = -11 -11 + -3x + 5x2 + -2x2 = 21 + 2x2 + -21 + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -11 + -3x + 3x2 = 21 + 2x2 + -21 + -2x2 Reorder the terms: -11 + -3x + 3x2 = 21 + -21 + 2x2 + -2x2 Combine like terms: 21 + -21 = 0 -11 + -3x + 3x2 = 0 + 2x2 + -2x2 -11 + -3x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -11 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + -1x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + -1x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + -1x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + -1x + x2 = 0 + 3.666666667 -1x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 -1x + x2 = 3.666666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3.666666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.666666667 + 0.25 Combine like terms: 3.666666667 + 0.25 = 3.916666667 0.25 + -1x + x2 = 3.916666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.916666667 Calculate the square root of the right side: 1.979057015 Break this problem into two subproblems by setting (x + -0.5) equal to 1.979057015 and -1.979057015.Subproblem 1
x + -0.5 = 1.979057015 Simplifying x + -0.5 = 1.979057015 Reorder the terms: -0.5 + x = 1.979057015 Solving -0.5 + x = 1.979057015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.979057015 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.979057015 + 0.5 x = 1.979057015 + 0.5 Combine like terms: 1.979057015 + 0.5 = 2.479057015 x = 2.479057015 Simplifying x = 2.479057015Subproblem 2
x + -0.5 = -1.979057015 Simplifying x + -0.5 = -1.979057015 Reorder the terms: -0.5 + x = -1.979057015 Solving -0.5 + x = -1.979057015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.979057015 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.979057015 + 0.5 x = -1.979057015 + 0.5 Combine like terms: -1.979057015 + 0.5 = -1.479057015 x = -1.479057015 Simplifying x = -1.479057015Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.479057015, -1.479057015}
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