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Simplifying x(x + -30) = 190 Reorder the terms: x(-30 + x) = 190 (-30 * x + x * x) = 190 (-30x + x2) = 190 Solving -30x + x2 = 190 Solving for variable 'x'. Reorder the terms: -190 + -30x + x2 = 190 + -190 Combine like terms: 190 + -190 = 0 -190 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + -30x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + -30x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + -30x + x2 = 0 + 190 -30x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 -30x + x2 = 190 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 = 190 + 225 Reorder the terms: 225 + -30x + x2 = 190 + 225 Combine like terms: 190 + 225 = 415 225 + -30x + x2 = 415 Factor a perfect square on the left side: (x + -15)(x + -15) = 415 Calculate the square root of the right side: 20.371548787 Break this problem into two subproblems by setting (x + -15) equal to 20.371548787 and -20.371548787.Subproblem 1
x + -15 = 20.371548787 Simplifying x + -15 = 20.371548787 Reorder the terms: -15 + x = 20.371548787 Solving -15 + x = 20.371548787 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 = 20.371548787 + 15 Combine like terms: -15 + 15 = 0 0 + x = 20.371548787 + 15 x = 20.371548787 + 15 Combine like terms: 20.371548787 + 15 = 35.371548787 x = 35.371548787 Simplifying x = 35.371548787Subproblem 2
x + -15 = -20.371548787 Simplifying x + -15 = -20.371548787 Reorder the terms: -15 + x = -20.371548787 Solving -15 + x = -20.371548787 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 = -20.371548787 + 15 Combine like terms: -15 + 15 = 0 0 + x = -20.371548787 + 15 x = -20.371548787 + 15 Combine like terms: -20.371548787 + 15 = -5.371548787 x = -5.371548787 Simplifying x = -5.371548787Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.371548787, -5.371548787}
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