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Simplifying 3x2 + -28 + 2x2 + -3x = 180 Reorder the terms: -28 + -3x + 3x2 + 2x2 = 180 Combine like terms: 3x2 + 2x2 = 5x2 -28 + -3x + 5x2 = 180 Solving -28 + -3x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: -28 + -180 + -3x + 5x2 = 180 + -180 Combine like terms: -28 + -180 = -208 -208 + -3x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -208 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -41.6 + -0.6x + x2 = 0 Move the constant term to the right: Add '41.6' to each side of the equation. -41.6 + -0.6x + 41.6 + x2 = 0 + 41.6 Reorder the terms: -41.6 + 41.6 + -0.6x + x2 = 0 + 41.6 Combine like terms: -41.6 + 41.6 = 0.0 0.0 + -0.6x + x2 = 0 + 41.6 -0.6x + x2 = 0 + 41.6 Combine like terms: 0 + 41.6 = 41.6 -0.6x + x2 = 41.6 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 41.6 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 41.6 + 0.09 Combine like terms: 41.6 + 0.09 = 41.69 0.09 + -0.6x + x2 = 41.69 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 41.69 Calculate the square root of the right side: 6.456779383 Break this problem into two subproblems by setting (x + -0.3) equal to 6.456779383 and -6.456779383.Subproblem 1
x + -0.3 = 6.456779383 Simplifying x + -0.3 = 6.456779383 Reorder the terms: -0.3 + x = 6.456779383 Solving -0.3 + x = 6.456779383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 6.456779383 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 6.456779383 + 0.3 x = 6.456779383 + 0.3 Combine like terms: 6.456779383 + 0.3 = 6.756779383 x = 6.756779383 Simplifying x = 6.756779383Subproblem 2
x + -0.3 = -6.456779383 Simplifying x + -0.3 = -6.456779383 Reorder the terms: -0.3 + x = -6.456779383 Solving -0.3 + x = -6.456779383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -6.456779383 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -6.456779383 + 0.3 x = -6.456779383 + 0.3 Combine like terms: -6.456779383 + 0.3 = -6.156779383 x = -6.156779383 Simplifying x = -6.156779383Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.756779383, -6.156779383}
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