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Simplifying 5x2 + -3x + 9 = 14 Reorder the terms: 9 + -3x + 5x2 = 14 Solving 9 + -3x + 5x2 = 14 Solving for variable 'x'. Reorder the terms: 9 + -14 + -3x + 5x2 = 14 + -14 Combine like terms: 9 + -14 = -5 -5 + -3x + 5x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -5 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -0.6x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.6x + x2 = 0 + 1 -0.6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.6x + x2 = 1 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 = 1 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1 + 0.09 Combine like terms: 1 + 0.09 = 1.09 0.09 + -0.6x + x2 = 1.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.09 Calculate the square root of the right side: 1.044030651 Break this problem into two subproblems by setting (x + -0.3) equal to 1.044030651 and -1.044030651.Subproblem 1
x + -0.3 = 1.044030651 Simplifying x + -0.3 = 1.044030651 Reorder the terms: -0.3 + x = 1.044030651 Solving -0.3 + x = 1.044030651 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 = 1.044030651 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.044030651 + 0.3 x = 1.044030651 + 0.3 Combine like terms: 1.044030651 + 0.3 = 1.344030651 x = 1.344030651 Simplifying x = 1.344030651Subproblem 2
x + -0.3 = -1.044030651 Simplifying x + -0.3 = -1.044030651 Reorder the terms: -0.3 + x = -1.044030651 Solving -0.3 + x = -1.044030651 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 = -1.044030651 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.044030651 + 0.3 x = -1.044030651 + 0.3 Combine like terms: -1.044030651 + 0.3 = -0.744030651 x = -0.744030651 Simplifying x = -0.744030651Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.344030651, -0.744030651}
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