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Simplifying 240 = 390 + -5x2 + 2x Reorder the terms: 240 = 390 + 2x + -5x2 Solving 240 = 390 + 2x + -5x2 Solving for variable 'x'. Combine like terms: 240 + -390 = -150 -150 + -2x + 5x2 = 390 + 2x + -5x2 + -390 + -2x + 5x2 Reorder the terms: -150 + -2x + 5x2 = 390 + -390 + 2x + -2x + -5x2 + 5x2 Combine like terms: 390 + -390 = 0 -150 + -2x + 5x2 = 0 + 2x + -2x + -5x2 + 5x2 -150 + -2x + 5x2 = 2x + -2x + -5x2 + 5x2 Combine like terms: 2x + -2x = 0 -150 + -2x + 5x2 = 0 + -5x2 + 5x2 -150 + -2x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -150 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -30 + -0.4x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -0.4x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -0.4x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -0.4x + x2 = 0 + 30 -0.4x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -0.4x + x2 = 30 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 30 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 30 + 0.04 Combine like terms: 30 + 0.04 = 30.04 0.04 + -0.4x + x2 = 30.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 30.04 Calculate the square root of the right side: 5.480875842 Break this problem into two subproblems by setting (x + -0.2) equal to 5.480875842 and -5.480875842.Subproblem 1
x + -0.2 = 5.480875842 Simplifying x + -0.2 = 5.480875842 Reorder the terms: -0.2 + x = 5.480875842 Solving -0.2 + x = 5.480875842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 5.480875842 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 5.480875842 + 0.2 x = 5.480875842 + 0.2 Combine like terms: 5.480875842 + 0.2 = 5.680875842 x = 5.680875842 Simplifying x = 5.680875842Subproblem 2
x + -0.2 = -5.480875842 Simplifying x + -0.2 = -5.480875842 Reorder the terms: -0.2 + x = -5.480875842 Solving -0.2 + x = -5.480875842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -5.480875842 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -5.480875842 + 0.2 x = -5.480875842 + 0.2 Combine like terms: -5.480875842 + 0.2 = -5.280875842 x = -5.280875842 Simplifying x = -5.280875842Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.680875842, -5.280875842}
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