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Simplifying 5x2 + -12x + -63 = 0 Reorder the terms: -63 + -12x + 5x2 = 0 Solving -63 + -12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + -2.4x + x2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + -2.4x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + -2.4x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + -2.4x + x2 = 0 + 12.6 -2.4x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 -2.4x + x2 = 12.6 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 = 12.6 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 12.6 + 1.44 Combine like terms: 12.6 + 1.44 = 14.04 1.44 + -2.4x + x2 = 14.04 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 14.04 Calculate the square root of the right side: 3.746998799 Break this problem into two subproblems by setting (x + -1.2) equal to 3.746998799 and -3.746998799.Subproblem 1
x + -1.2 = 3.746998799 Simplifying x + -1.2 = 3.746998799 Reorder the terms: -1.2 + x = 3.746998799 Solving -1.2 + x = 3.746998799 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 = 3.746998799 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 3.746998799 + 1.2 x = 3.746998799 + 1.2 Combine like terms: 3.746998799 + 1.2 = 4.946998799 x = 4.946998799 Simplifying x = 4.946998799Subproblem 2
x + -1.2 = -3.746998799 Simplifying x + -1.2 = -3.746998799 Reorder the terms: -1.2 + x = -3.746998799 Solving -1.2 + x = -3.746998799 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 = -3.746998799 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -3.746998799 + 1.2 x = -3.746998799 + 1.2 Combine like terms: -3.746998799 + 1.2 = -2.546998799 x = -2.546998799 Simplifying x = -2.546998799Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.946998799, -2.546998799}
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