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Simplifying -0.016x2 + 1.152x + -15.2 = 0 Reorder the terms: -15.2 + 1.152x + -0.016x2 = 0 Solving -15.2 + 1.152x + -0.016x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.016 the coefficient of the squared term: Divide each side by '-0.016'. 950 + -72x + x2 = 0 Move the constant term to the right: Add '-950' to each side of the equation. 950 + -72x + -950 + x2 = 0 + -950 Reorder the terms: 950 + -950 + -72x + x2 = 0 + -950 Combine like terms: 950 + -950 = 0 0 + -72x + x2 = 0 + -950 -72x + x2 = 0 + -950 Combine like terms: 0 + -950 = -950 -72x + x2 = -950 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = -950 + 1296 Reorder the terms: 1296 + -72x + x2 = -950 + 1296 Combine like terms: -950 + 1296 = 346 1296 + -72x + x2 = 346 Factor a perfect square on the left side: (x + -36)(x + -36) = 346 Calculate the square root of the right side: 18.601075238 Break this problem into two subproblems by setting (x + -36) equal to 18.601075238 and -18.601075238.Subproblem 1
x + -36 = 18.601075238 Simplifying x + -36 = 18.601075238 Reorder the terms: -36 + x = 18.601075238 Solving -36 + x = 18.601075238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 18.601075238 + 36 Combine like terms: -36 + 36 = 0 0 + x = 18.601075238 + 36 x = 18.601075238 + 36 Combine like terms: 18.601075238 + 36 = 54.601075238 x = 54.601075238 Simplifying x = 54.601075238Subproblem 2
x + -36 = -18.601075238 Simplifying x + -36 = -18.601075238 Reorder the terms: -36 + x = -18.601075238 Solving -36 + x = -18.601075238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -18.601075238 + 36 Combine like terms: -36 + 36 = 0 0 + x = -18.601075238 + 36 x = -18.601075238 + 36 Combine like terms: -18.601075238 + 36 = 17.398924762 x = 17.398924762 Simplifying x = 17.398924762Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.601075238, 17.398924762}
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