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Simplifying 17x(4x + -9) = 61 Reorder the terms: 17x(-9 + 4x) = 61 (-9 * 17x + 4x * 17x) = 61 (-153x + 68x2) = 61 Solving -153x + 68x2 = 61 Solving for variable 'x'. Reorder the terms: -61 + -153x + 68x2 = 61 + -61 Combine like terms: 61 + -61 = 0 -61 + -153x + 68x2 = 0 Begin completing the square. Divide all terms by 68 the coefficient of the squared term: Divide each side by '68'. -0.8970588235 + -2.25x + x2 = 0 Move the constant term to the right: Add '0.8970588235' to each side of the equation. -0.8970588235 + -2.25x + 0.8970588235 + x2 = 0 + 0.8970588235 Reorder the terms: -0.8970588235 + 0.8970588235 + -2.25x + x2 = 0 + 0.8970588235 Combine like terms: -0.8970588235 + 0.8970588235 = 0.0000000000 0.0000000000 + -2.25x + x2 = 0 + 0.8970588235 -2.25x + x2 = 0 + 0.8970588235 Combine like terms: 0 + 0.8970588235 = 0.8970588235 -2.25x + x2 = 0.8970588235 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 0.8970588235 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 0.8970588235 + 1.265625 Combine like terms: 0.8970588235 + 1.265625 = 2.1626838235 1.265625 + -2.25x + x2 = 2.1626838235 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 2.1626838235 Calculate the square root of the right side: 1.470606618 Break this problem into two subproblems by setting (x + -1.125) equal to 1.470606618 and -1.470606618.Subproblem 1
x + -1.125 = 1.470606618 Simplifying x + -1.125 = 1.470606618 Reorder the terms: -1.125 + x = 1.470606618 Solving -1.125 + x = 1.470606618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.470606618 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.470606618 + 1.125 x = 1.470606618 + 1.125 Combine like terms: 1.470606618 + 1.125 = 2.595606618 x = 2.595606618 Simplifying x = 2.595606618Subproblem 2
x + -1.125 = -1.470606618 Simplifying x + -1.125 = -1.470606618 Reorder the terms: -1.125 + x = -1.470606618 Solving -1.125 + x = -1.470606618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.470606618 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.470606618 + 1.125 x = -1.470606618 + 1.125 Combine like terms: -1.470606618 + 1.125 = -0.345606618 x = -0.345606618 Simplifying x = -0.345606618Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.595606618, -0.345606618}
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