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Simplifying 10x2 + -3x + -270 = 0 Reorder the terms: -270 + -3x + 10x2 = 0 Solving -270 + -3x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -27 + -0.3x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -0.3x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -0.3x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -0.3x + x2 = 0 + 27 -0.3x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -0.3x + x2 = 27 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 27 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 27 + 0.0225 Combine like terms: 27 + 0.0225 = 27.0225 0.0225 + -0.3x + x2 = 27.0225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 27.0225 Calculate the square root of the right side: 5.198317035 Break this problem into two subproblems by setting (x + -0.15) equal to 5.198317035 and -5.198317035.Subproblem 1
x + -0.15 = 5.198317035 Simplifying x + -0.15 = 5.198317035 Reorder the terms: -0.15 + x = 5.198317035 Solving -0.15 + x = 5.198317035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 5.198317035 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 5.198317035 + 0.15 x = 5.198317035 + 0.15 Combine like terms: 5.198317035 + 0.15 = 5.348317035 x = 5.348317035 Simplifying x = 5.348317035Subproblem 2
x + -0.15 = -5.198317035 Simplifying x + -0.15 = -5.198317035 Reorder the terms: -0.15 + x = -5.198317035 Solving -0.15 + x = -5.198317035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -5.198317035 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -5.198317035 + 0.15 x = -5.198317035 + 0.15 Combine like terms: -5.198317035 + 0.15 = -5.048317035 x = -5.048317035 Simplifying x = -5.048317035Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.348317035, -5.048317035}
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