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Simplifying 5x2 + -4x + 3 = 17 Reorder the terms: 3 + -4x + 5x2 = 17 Solving 3 + -4x + 5x2 = 17 Solving for variable 'x'. Reorder the terms: 3 + -17 + -4x + 5x2 = 17 + -17 Combine like terms: 3 + -17 = -14 -14 + -4x + 5x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -14 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -0.8x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -0.8x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -0.8x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -0.8x + x2 = 0 + 2.8 -0.8x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -0.8x + x2 = 2.8 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 2.8 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 2.8 + 0.16 Combine like terms: 2.8 + 0.16 = 2.96 0.16 + -0.8x + x2 = 2.96 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 2.96 Calculate the square root of the right side: 1.720465053 Break this problem into two subproblems by setting (x + -0.4) equal to 1.720465053 and -1.720465053.Subproblem 1
x + -0.4 = 1.720465053 Simplifying x + -0.4 = 1.720465053 Reorder the terms: -0.4 + x = 1.720465053 Solving -0.4 + x = 1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.720465053 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.720465053 + 0.4 x = 1.720465053 + 0.4 Combine like terms: 1.720465053 + 0.4 = 2.120465053 x = 2.120465053 Simplifying x = 2.120465053Subproblem 2
x + -0.4 = -1.720465053 Simplifying x + -0.4 = -1.720465053 Reorder the terms: -0.4 + x = -1.720465053 Solving -0.4 + x = -1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.720465053 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.720465053 + 0.4 x = -1.720465053 + 0.4 Combine like terms: -1.720465053 + 0.4 = -1.320465053 x = -1.320465053 Simplifying x = -1.320465053Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.120465053, -1.320465053}
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