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Simplifying 5x2 + -24x + -4 = 0 Reorder the terms: -4 + -24x + 5x2 = 0 Solving -4 + -24x + 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'. -0.8 + -4.8x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -4.8x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -4.8x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -4.8x + x2 = 0 + 0.8 -4.8x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -4.8x + x2 = 0.8 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = 0.8 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = 0.8 + 5.76 Combine like terms: 0.8 + 5.76 = 6.56 5.76 + -4.8x + x2 = 6.56 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 6.56 Calculate the square root of the right side: 2.561249695 Break this problem into two subproblems by setting (x + -2.4) equal to 2.561249695 and -2.561249695.Subproblem 1
x + -2.4 = 2.561249695 Simplifying x + -2.4 = 2.561249695 Reorder the terms: -2.4 + x = 2.561249695 Solving -2.4 + x = 2.561249695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 2.561249695 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 2.561249695 + 2.4 x = 2.561249695 + 2.4 Combine like terms: 2.561249695 + 2.4 = 4.961249695 x = 4.961249695 Simplifying x = 4.961249695Subproblem 2
x + -2.4 = -2.561249695 Simplifying x + -2.4 = -2.561249695 Reorder the terms: -2.4 + x = -2.561249695 Solving -2.4 + x = -2.561249695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -2.561249695 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -2.561249695 + 2.4 x = -2.561249695 + 2.4 Combine like terms: -2.561249695 + 2.4 = -0.161249695 x = -0.161249695 Simplifying x = -0.161249695Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.961249695, -0.161249695}
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