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Simplifying 7x2 + 4x + -25 = 0 Reorder the terms: -25 + 4x + 7x2 = 0 Solving -25 + 4x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.571428571 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + 0.5714285714x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + 0.5714285714x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + 3.571428571 0.5714285714x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 0.5714285714x + x2 = 3.571428571 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 3.571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 3.571428571 + 0.08163265305 Combine like terms: 3.571428571 + 0.08163265305 = 3.65306122405 0.08163265305 + 0.5714285714x + x2 = 3.65306122405 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 3.65306122405 Calculate the square root of the right side: 1.911298308 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 1.911298308 and -1.911298308.Subproblem 1
x + 0.2857142857 = 1.911298308 Simplifying x + 0.2857142857 = 1.911298308 Reorder the terms: 0.2857142857 + x = 1.911298308 Solving 0.2857142857 + x = 1.911298308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 1.911298308 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 1.911298308 + -0.2857142857 x = 1.911298308 + -0.2857142857 Combine like terms: 1.911298308 + -0.2857142857 = 1.6255840223 x = 1.6255840223 Simplifying x = 1.6255840223Subproblem 2
x + 0.2857142857 = -1.911298308 Simplifying x + 0.2857142857 = -1.911298308 Reorder the terms: 0.2857142857 + x = -1.911298308 Solving 0.2857142857 + x = -1.911298308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -1.911298308 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -1.911298308 + -0.2857142857 x = -1.911298308 + -0.2857142857 Combine like terms: -1.911298308 + -0.2857142857 = -2.1970125937 x = -2.1970125937 Simplifying x = -2.1970125937Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6255840223, -2.1970125937}
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