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Simplifying x2 + 4(x + 5) = 400 Reorder the terms: x2 + 4(5 + x) = 400 x2 + (5 * 4 + x * 4) = 400 x2 + (20 + 4x) = 400 Reorder the terms: 20 + 4x + x2 = 400 Solving 20 + 4x + x2 = 400 Solving for variable 'x'. Reorder the terms: 20 + -400 + 4x + x2 = 400 + -400 Combine like terms: 20 + -400 = -380 -380 + 4x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -380 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '380' to each side of the equation. -380 + 4x + 380 + x2 = 0 + 380 Reorder the terms: -380 + 380 + 4x + x2 = 0 + 380 Combine like terms: -380 + 380 = 0 0 + 4x + x2 = 0 + 380 4x + x2 = 0 + 380 Combine like terms: 0 + 380 = 380 4x + x2 = 380 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 380 + 4 Reorder the terms: 4 + 4x + x2 = 380 + 4 Combine like terms: 380 + 4 = 384 4 + 4x + x2 = 384 Factor a perfect square on the left side: (x + 2)(x + 2) = 384 Calculate the square root of the right side: 19.595917942 Break this problem into two subproblems by setting (x + 2) equal to 19.595917942 and -19.595917942.Subproblem 1
x + 2 = 19.595917942 Simplifying x + 2 = 19.595917942 Reorder the terms: 2 + x = 19.595917942 Solving 2 + x = 19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 19.595917942 + -2 Combine like terms: 2 + -2 = 0 0 + x = 19.595917942 + -2 x = 19.595917942 + -2 Combine like terms: 19.595917942 + -2 = 17.595917942 x = 17.595917942 Simplifying x = 17.595917942Subproblem 2
x + 2 = -19.595917942 Simplifying x + 2 = -19.595917942 Reorder the terms: 2 + x = -19.595917942 Solving 2 + x = -19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -19.595917942 + -2 Combine like terms: 2 + -2 = 0 0 + x = -19.595917942 + -2 x = -19.595917942 + -2 Combine like terms: -19.595917942 + -2 = -21.595917942 x = -21.595917942 Simplifying x = -21.595917942Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.595917942, -21.595917942}
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