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Simplifying x(x + -7)(x + -7) = 50x Reorder the terms: x(-7 + x)(x + -7) = 50x Reorder the terms: x(-7 + x)(-7 + x) = 50x Multiply (-7 + x) * (-7 + x) x(-7(-7 + x) + x(-7 + x)) = 50x x((-7 * -7 + x * -7) + x(-7 + x)) = 50x x((49 + -7x) + x(-7 + x)) = 50x x(49 + -7x + (-7 * x + x * x)) = 50x x(49 + -7x + (-7x + x2)) = 50x Combine like terms: -7x + -7x = -14x x(49 + -14x + x2) = 50x (49 * x + -14x * x + x2 * x) = 50x (49x + -14x2 + x3) = 50x Solving 49x + -14x2 + x3 = 50x Solving for variable 'x'. Reorder the terms: 49x + -50x + -14x2 + x3 = 50x + -50x Combine like terms: 49x + -50x = -1x -1x + -14x2 + x3 = 50x + -50x Combine like terms: 50x + -50x = 0 -1x + -14x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + -14x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + -14x + x2)' equal to zero and attempt to solve: Simplifying -1 + -14x + x2 = 0 Solving -1 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -14x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -14x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -14x + x2 = 0 + 1 -14x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -14x + x2 = 1 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 1 + 49 Reorder the terms: 49 + -14x + x2 = 1 + 49 Combine like terms: 1 + 49 = 50 49 + -14x + x2 = 50 Factor a perfect square on the left side: (x + -7)(x + -7) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -7) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -7 = 7.071067812 Simplifying x + -7 = 7.071067812 Reorder the terms: -7 + x = 7.071067812 Solving -7 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.071067812 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.071067812 + 7 x = 7.071067812 + 7 Combine like terms: 7.071067812 + 7 = 14.071067812 x = 14.071067812 Simplifying x = 14.071067812Subproblem 2
x + -7 = -7.071067812 Simplifying x + -7 = -7.071067812 Reorder the terms: -7 + x = -7.071067812 Solving -7 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.071067812 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.071067812 + 7 x = -7.071067812 + 7 Combine like terms: -7.071067812 + 7 = -0.071067812 x = -0.071067812 Simplifying x = -0.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.071067812, -0.071067812}Solution
x = {0, 14.071067812, -0.071067812}
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