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Simplifying -25x2 + 60x + 32 = 0 Reorder the terms: 32 + 60x + -25x2 = 0 Solving 32 + 60x + -25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -1.28 + -2.4x + x2 = 0 Move the constant term to the right: Add '1.28' to each side of the equation. -1.28 + -2.4x + 1.28 + x2 = 0 + 1.28 Reorder the terms: -1.28 + 1.28 + -2.4x + x2 = 0 + 1.28 Combine like terms: -1.28 + 1.28 = 0.00 0.00 + -2.4x + x2 = 0 + 1.28 -2.4x + x2 = 0 + 1.28 Combine like terms: 0 + 1.28 = 1.28 -2.4x + x2 = 1.28 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 1.28 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 1.28 + 1.44 Combine like terms: 1.28 + 1.44 = 2.72 1.44 + -2.4x + x2 = 2.72 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 2.72 Calculate the square root of the right side: 1.64924225 Break this problem into two subproblems by setting (x + -1.2) equal to 1.64924225 and -1.64924225.Subproblem 1
x + -1.2 = 1.64924225 Simplifying x + -1.2 = 1.64924225 Reorder the terms: -1.2 + x = 1.64924225 Solving -1.2 + x = 1.64924225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.64924225 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.64924225 + 1.2 x = 1.64924225 + 1.2 Combine like terms: 1.64924225 + 1.2 = 2.84924225 x = 2.84924225 Simplifying x = 2.84924225Subproblem 2
x + -1.2 = -1.64924225 Simplifying x + -1.2 = -1.64924225 Reorder the terms: -1.2 + x = -1.64924225 Solving -1.2 + x = -1.64924225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.64924225 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.64924225 + 1.2 x = -1.64924225 + 1.2 Combine like terms: -1.64924225 + 1.2 = -0.44924225 x = -0.44924225 Simplifying x = -0.44924225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.84924225, -0.44924225}
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