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Simplifying -5x2 + 1.5x + 2 = 0.92 Reorder the terms: 2 + 1.5x + -5x2 = 0.92 Solving 2 + 1.5x + -5x2 = 0.92 Solving for variable 'x'. Reorder the terms: 2 + -0.92 + 1.5x + -5x2 = 0.92 + -0.92 Combine like terms: 2 + -0.92 = 1.08 1.08 + 1.5x + -5x2 = 0.92 + -0.92 Combine like terms: 0.92 + -0.92 = 0.00 1.08 + 1.5x + -5x2 = 0.00 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.216 + -0.3x + x2 = 0.00 Move the constant term to the right: Add '0.216' to each side of the equation. -0.216 + -0.3x + 0.216 + x2 = 0.00 + 0.216 Reorder the terms: -0.216 + 0.216 + -0.3x + x2 = 0.00 + 0.216 Combine like terms: -0.216 + 0.216 = 0.000 0.000 + -0.3x + x2 = 0.00 + 0.216 -0.3x + x2 = 0.00 + 0.216 Combine like terms: 0.00 + 0.216 = 0.216 -0.3x + x2 = 0.216 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 = 0.216 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.216 + 0.0225 Combine like terms: 0.216 + 0.0225 = 0.2385 0.0225 + -0.3x + x2 = 0.2385 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.2385 Calculate the square root of the right side: 0.488364618 Break this problem into two subproblems by setting (x + -0.15) equal to 0.488364618 and -0.488364618.Subproblem 1
x + -0.15 = 0.488364618 Simplifying x + -0.15 = 0.488364618 Reorder the terms: -0.15 + x = 0.488364618 Solving -0.15 + x = 0.488364618 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 = 0.488364618 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.488364618 + 0.15 x = 0.488364618 + 0.15 Combine like terms: 0.488364618 + 0.15 = 0.638364618 x = 0.638364618 Simplifying x = 0.638364618Subproblem 2
x + -0.15 = -0.488364618 Simplifying x + -0.15 = -0.488364618 Reorder the terms: -0.15 + x = -0.488364618 Solving -0.15 + x = -0.488364618 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 = -0.488364618 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.488364618 + 0.15 x = -0.488364618 + 0.15 Combine like terms: -0.488364618 + 0.15 = -0.338364618 x = -0.338364618 Simplifying x = -0.338364618Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.638364618, -0.338364618}
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