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Simplifying x2 + -16 = 40x + -10 Reorder the terms: -16 + x2 = 40x + -10 Reorder the terms: -16 + x2 = -10 + 40x Solving -16 + x2 = -10 + 40x Solving for variable 'x'. Reorder the terms: -16 + 10 + -40x + x2 = -10 + 40x + 10 + -40x Combine like terms: -16 + 10 = -6 -6 + -40x + x2 = -10 + 40x + 10 + -40x Reorder the terms: -6 + -40x + x2 = -10 + 10 + 40x + -40x Combine like terms: -10 + 10 = 0 -6 + -40x + x2 = 0 + 40x + -40x -6 + -40x + x2 = 40x + -40x Combine like terms: 40x + -40x = 0 -6 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -40x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -40x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -40x + x2 = 0 + 6 -40x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -40x + x2 = 6 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 6 + 400 Reorder the terms: 400 + -40x + x2 = 6 + 400 Combine like terms: 6 + 400 = 406 400 + -40x + x2 = 406 Factor a perfect square on the left side: (x + -20)(x + -20) = 406 Calculate the square root of the right side: 20.14944168 Break this problem into two subproblems by setting (x + -20) equal to 20.14944168 and -20.14944168.Subproblem 1
x + -20 = 20.14944168 Simplifying x + -20 = 20.14944168 Reorder the terms: -20 + x = 20.14944168 Solving -20 + x = 20.14944168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 20.14944168 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.14944168 + 20 x = 20.14944168 + 20 Combine like terms: 20.14944168 + 20 = 40.14944168 x = 40.14944168 Simplifying x = 40.14944168Subproblem 2
x + -20 = -20.14944168 Simplifying x + -20 = -20.14944168 Reorder the terms: -20 + x = -20.14944168 Solving -20 + x = -20.14944168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -20.14944168 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.14944168 + 20 x = -20.14944168 + 20 Combine like terms: -20.14944168 + 20 = -0.14944168 x = -0.14944168 Simplifying x = -0.14944168Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.14944168, -0.14944168}
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