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Simplifying 5x2 + -15x + 2.16 = 0 Reorder the terms: 2.16 + -15x + 5x2 = 0 Solving 2.16 + -15x + 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'. 0.432 + -3x + x2 = 0 Move the constant term to the right: Add '-0.432' to each side of the equation. 0.432 + -3x + -0.432 + x2 = 0 + -0.432 Reorder the terms: 0.432 + -0.432 + -3x + x2 = 0 + -0.432 Combine like terms: 0.432 + -0.432 = 0.000 0.000 + -3x + x2 = 0 + -0.432 -3x + x2 = 0 + -0.432 Combine like terms: 0 + -0.432 = -0.432 -3x + x2 = -0.432 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.432 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.432 + 2.25 Combine like terms: -0.432 + 2.25 = 1.818 2.25 + -3x + x2 = 1.818 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.818 Calculate the square root of the right side: 1.348332303 Break this problem into two subproblems by setting (x + -1.5) equal to 1.348332303 and -1.348332303.Subproblem 1
x + -1.5 = 1.348332303 Simplifying x + -1.5 = 1.348332303 Reorder the terms: -1.5 + x = 1.348332303 Solving -1.5 + x = 1.348332303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.348332303 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.348332303 + 1.5 x = 1.348332303 + 1.5 Combine like terms: 1.348332303 + 1.5 = 2.848332303 x = 2.848332303 Simplifying x = 2.848332303Subproblem 2
x + -1.5 = -1.348332303 Simplifying x + -1.5 = -1.348332303 Reorder the terms: -1.5 + x = -1.348332303 Solving -1.5 + x = -1.348332303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.348332303 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.348332303 + 1.5 x = -1.348332303 + 1.5 Combine like terms: -1.348332303 + 1.5 = 0.151667697 x = 0.151667697 Simplifying x = 0.151667697Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.848332303, 0.151667697}
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