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Simplifying (2x + 10)(x + -4) = 21 Reorder the terms: (10 + 2x)(x + -4) = 21 Reorder the terms: (10 + 2x)(-4 + x) = 21 Multiply (10 + 2x) * (-4 + x) (10(-4 + x) + 2x * (-4 + x)) = 21 ((-4 * 10 + x * 10) + 2x * (-4 + x)) = 21 ((-40 + 10x) + 2x * (-4 + x)) = 21 (-40 + 10x + (-4 * 2x + x * 2x)) = 21 (-40 + 10x + (-8x + 2x2)) = 21 Combine like terms: 10x + -8x = 2x (-40 + 2x + 2x2) = 21 Solving -40 + 2x + 2x2 = 21 Solving for variable 'x'. Reorder the terms: -40 + -21 + 2x + 2x2 = 21 + -21 Combine like terms: -40 + -21 = -61 -61 + 2x + 2x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -61 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30.5 + x + x2 = 0 Move the constant term to the right: Add '30.5' to each side of the equation. -30.5 + x + 30.5 + x2 = 0 + 30.5 Reorder the terms: -30.5 + 30.5 + x + x2 = 0 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + x + x2 = 0 + 30.5 x + x2 = 0 + 30.5 Combine like terms: 0 + 30.5 = 30.5 x + x2 = 30.5 The x term is x. 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. + 0.25 + x2 = 30.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 30.5 + 0.25 Combine like terms: 30.5 + 0.25 = 30.75 1.25 + x2 = 30.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 30.75 Calculate the square root of the right side: 5.545268253 Break this problem into two subproblems by setting (x + 0.5) equal to 5.545268253 and -5.545268253.Subproblem 1
x + 0.5 = 5.545268253 Simplifying x + 0.5 = 5.545268253 Reorder the terms: 0.5 + x = 5.545268253 Solving 0.5 + x = 5.545268253 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 = 5.545268253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.545268253 + -0.5 x = 5.545268253 + -0.5 Combine like terms: 5.545268253 + -0.5 = 5.045268253 x = 5.045268253 Simplifying x = 5.045268253Subproblem 2
x + 0.5 = -5.545268253 Simplifying x + 0.5 = -5.545268253 Reorder the terms: 0.5 + x = -5.545268253 Solving 0.5 + x = -5.545268253 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 = -5.545268253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.545268253 + -0.5 x = -5.545268253 + -0.5 Combine like terms: -5.545268253 + -0.5 = -6.045268253 x = -6.045268253 Simplifying x = -6.045268253Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.045268253, -6.045268253}
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