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Simplifying x2 + 4x + -10 = 400 Reorder the terms: -10 + 4x + x2 = 400 Solving -10 + 4x + x2 = 400 Solving for variable 'x'. Reorder the terms: -10 + -400 + 4x + x2 = 400 + -400 Combine like terms: -10 + -400 = -410 -410 + 4x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -410 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '410' to each side of the equation. -410 + 4x + 410 + x2 = 0 + 410 Reorder the terms: -410 + 410 + 4x + x2 = 0 + 410 Combine like terms: -410 + 410 = 0 0 + 4x + x2 = 0 + 410 4x + x2 = 0 + 410 Combine like terms: 0 + 410 = 410 4x + x2 = 410 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 = 410 + 4 Reorder the terms: 4 + 4x + x2 = 410 + 4 Combine like terms: 410 + 4 = 414 4 + 4x + x2 = 414 Factor a perfect square on the left side: (x + 2)(x + 2) = 414 Calculate the square root of the right side: 20.346989949 Break this problem into two subproblems by setting (x + 2) equal to 20.346989949 and -20.346989949.Subproblem 1
x + 2 = 20.346989949 Simplifying x + 2 = 20.346989949 Reorder the terms: 2 + x = 20.346989949 Solving 2 + x = 20.346989949 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 = 20.346989949 + -2 Combine like terms: 2 + -2 = 0 0 + x = 20.346989949 + -2 x = 20.346989949 + -2 Combine like terms: 20.346989949 + -2 = 18.346989949 x = 18.346989949 Simplifying x = 18.346989949Subproblem 2
x + 2 = -20.346989949 Simplifying x + 2 = -20.346989949 Reorder the terms: 2 + x = -20.346989949 Solving 2 + x = -20.346989949 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 = -20.346989949 + -2 Combine like terms: 2 + -2 = 0 0 + x = -20.346989949 + -2 x = -20.346989949 + -2 Combine like terms: -20.346989949 + -2 = -22.346989949 x = -22.346989949 Simplifying x = -22.346989949Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.346989949, -22.346989949}
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