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Simplifying x2 + -30x = 10 Reorder the terms: -30x + x2 = 10 Solving -30x + x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -30x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -30x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -30x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -30x + x2 = 0 + 10 -30x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -30x + x2 = 10 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 10 + 225 Reorder the terms: 225 + -30x + x2 = 10 + 225 Combine like terms: 10 + 225 = 235 225 + -30x + x2 = 235 Factor a perfect square on the left side: (x + -15)(x + -15) = 235 Calculate the square root of the right side: 15.329709717 Break this problem into two subproblems by setting (x + -15) equal to 15.329709717 and -15.329709717.Subproblem 1
x + -15 = 15.329709717 Simplifying x + -15 = 15.329709717 Reorder the terms: -15 + x = 15.329709717 Solving -15 + x = 15.329709717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 15.329709717 + 15 Combine like terms: -15 + 15 = 0 0 + x = 15.329709717 + 15 x = 15.329709717 + 15 Combine like terms: 15.329709717 + 15 = 30.329709717 x = 30.329709717 Simplifying x = 30.329709717Subproblem 2
x + -15 = -15.329709717 Simplifying x + -15 = -15.329709717 Reorder the terms: -15 + x = -15.329709717 Solving -15 + x = -15.329709717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -15.329709717 + 15 Combine like terms: -15 + 15 = 0 0 + x = -15.329709717 + 15 x = -15.329709717 + 15 Combine like terms: -15.329709717 + 15 = -0.329709717 x = -0.329709717 Simplifying x = -0.329709717Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.329709717, -0.329709717}
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