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Simplifying (2x2 + -23x) + (3x2 + 60) = 90 Reorder the terms: (-23x + 2x2) + (3x2 + 60) = 90 Remove parenthesis around (-23x + 2x2) -23x + 2x2 + (3x2 + 60) = 90 Reorder the terms: -23x + 2x2 + (60 + 3x2) = 90 Remove parenthesis around (60 + 3x2) -23x + 2x2 + 60 + 3x2 = 90 Reorder the terms: 60 + -23x + 2x2 + 3x2 = 90 Combine like terms: 2x2 + 3x2 = 5x2 60 + -23x + 5x2 = 90 Solving 60 + -23x + 5x2 = 90 Solving for variable 'x'. Reorder the terms: 60 + -90 + -23x + 5x2 = 90 + -90 Combine like terms: 60 + -90 = -30 -30 + -23x + 5x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -30 + -23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + -4.6x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -4.6x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -4.6x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4.6x + x2 = 0 + 6 -4.6x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4.6x + x2 = 6 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 6 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 6 + 5.29 Combine like terms: 6 + 5.29 = 11.29 5.29 + -4.6x + x2 = 11.29 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 11.29 Calculate the square root of the right side: 3.360059523 Break this problem into two subproblems by setting (x + -2.3) equal to 3.360059523 and -3.360059523.Subproblem 1
x + -2.3 = 3.360059523 Simplifying x + -2.3 = 3.360059523 Reorder the terms: -2.3 + x = 3.360059523 Solving -2.3 + x = 3.360059523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 3.360059523 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 3.360059523 + 2.3 x = 3.360059523 + 2.3 Combine like terms: 3.360059523 + 2.3 = 5.660059523 x = 5.660059523 Simplifying x = 5.660059523Subproblem 2
x + -2.3 = -3.360059523 Simplifying x + -2.3 = -3.360059523 Reorder the terms: -2.3 + x = -3.360059523 Solving -2.3 + x = -3.360059523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -3.360059523 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -3.360059523 + 2.3 x = -3.360059523 + 2.3 Combine like terms: -3.360059523 + 2.3 = -1.060059523 x = -1.060059523 Simplifying x = -1.060059523Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.660059523, -1.060059523}
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